Calculus question and answers for November 21, 2023
- Q What is a coterminal angle of 22?/3?(a) 60(b)120(c) 240(d)300
- Q Let F be the set of functions of the form f(x) = A sin(x) + B cos(2x), where A, B are some real constants. Show that there must exist exactly...
- Q Solve sin^2(x) = 4 cos(x) for all solutions 0 ? x < 2?.x =Give your answers as values accurate to at least two decimal places in a list separated by...
- Q Triangle EFG has vertices El-11), F(3.1) and G(45) Find the coordinates of the image of point Fafter a reflection across the x-axis.
- Q The function f(x)=- 2x^3 +27x^2 - 108x + 10 has one local minimum and one local maximum.This function has a local minimum at x =_______________with value ___________and a local maximum...
- Q Jocelyn invested $56,000 in an account paying an interest rate of 7(3/8)% compounded continuously. Oliver invested $56,000 in an account paying an interest rate of 7(1/4)% compounded monthly. After 13...
- Q The function f(x) = 2x^3 27x + 84x 3 has two critical numbers.The smaller one is x =and the larger one is x =
- Q Determine the Cartesian equation of the plane that contains the points A(-2, 3, 1), B(3,4,5), and C(1, 1, 0).
- Q Harold uses the binomial theorem to expand the binomial.(a) What is the sum in summation notation that he uses to express the expansion?Write the simplified terms of the expansion.
- Q Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.y = In(x),...
- Q Find the average value ha of the function h on the given interval.avehave=h(u):12In(u)U(3.78656)[1, 7]
- Q An acute angle, o, is in a right triangle such that cos?=24/25. What is the value of csc ?? (a)7/24 (b)7/25 (c)25/7 (d)25/24
- Q Use the table below to find the limit, if it exists. If the limit does not exist type DNE. If you get infinity, you must type out the entire word,...
- Q lim (cos? - sin?)/(cos? - sin?) = ?->?/4(A) - 1(B) 0(C) ?2(D) 1(E)1/?2
- Q If a curve is defined by the parametric equations x(t) = 2t and y(t) = -4t - 2 over the interval- 2 ? t ? 2, which of the following...
- Q Find the antiderivative for the function f(x) = 3x(x + 1)?dx.
- Q The graph of the equation x + y - 2x - 6y = 21 is:(A) a circle(B) an ellipse(C) a hyperbola(D) a parabola(E) a sphere
- Q Find the following limits for the rational function f(x)=x+2/(4x -16) and justify your answers. If the limit does not exist, state so and show or explain why it does not...
- Q Which of the following is a solution to the equation sinx - cosx = 1?(A) x = 0(B) x = ?/6(C) x = ?/4(D) x = ?/2(E) x = ?
- Q Which of the following statements is NOT true about the curve defined by the parametric equations x(t) = 12 cos ?t and y(t) = 12 sin?t?(A) The curve is centered...
- Q If lim f(x) = 5 and lim g(x) = 3, then lim [g(x) = f(x)] = (A)- 2(B) 0(C) 2(D) 3(E) 5
- Q Sebastian invested $7,100 in an account paying an interest rate of 81% compounded monthly. Eva invested $7,100 in an account paying an interest rate of 81% compounded continuously. After 5...
- Q A petroleum company is making a cylindrical oil drum. The drum must hold 1.9 m of liquid. The drum must be taller than it is wide, but no more than...
- Q Find the first five terms of the sequence of partial sums. (Round your answers to four decimal places.)? (-5)?+s?=s?=s?=s?=s?=
- Q Let h(x) = 2x - x.Use the limit definition of the derivative to differentiate h.h'(x) = ____________Determine the slope of h at x = -3.h'(-3) =
- Q The limit below represents f'(c) for some function f and real number c.Iim [-1+(-2+?x)^2+9]/?x?x?0a)Determine the function f. f(x) =b)Determine the value of c. C=
- Q Consider the following repeating decimal.(a) Write the repeating decimal as a geometric series. n=0(b) Write the sum of the series as the ratio of two integers.
- Q In which quadrant does ? lie if the following statements are true:sin ? > ? and cos ? > ?A)Quadrant IB) Quadrant IIC) Quadrant IIID) Quadrant IV
- Q Evaluate the following limits. Justify each step. If the limit does not exist, explain why.a) lim 2ln|x + 2| ? ln(x^4 + 4x + 4x)b) lim sin(5x) csc (7x)c) lim(16x^3-2x^2+1)^(1/2)/(1+x^6)^(1/4)
- Q A rectangular paperboard measuring 30 in long and 20 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains...
- Q Find the nth Taylor polynomial for the function, centered at c.f(x) =1/x n = 4, c = 2P?(x) =
- Q Martha Stewart is designing a box for her cat to sleep in. It has 4 sides and a bottom but no top. The plush material for the square bottom of...
- Q Find the distance between the pair of points (3.3,7.2) and (-0.7,5.2). If numbersplaces.The distance between the given points is ________ units.
- Q Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.)y = ?2xupper...
- Q Use the Integral Test to determine the convergence or divergence of the p-series.? 1???1?(a) converges(b) diverges
- Q Determine if the following series are convergent or divergent. Justify your steps and state which test you are using. When necessary, make sure you check the hypotheses of the test...
- Q Decide whether the integral is improper.? sin(x)/26+x dx(a)proper(b)improperExplain your reasoning. (Select all that apply.)(a)The limits of integration are both finite.(b)The integrand is continuous on (-?, ?).(c)The integrand is not continuous...
- Q Write as a single logarithm. Simplify.2 log? u- log? v =
- Q Evaluate the following integrals.(a) ?(4x + 1)/(x-2)(x - 3) dx(b) (?x)ln(?x) dx(c)(x? + x + 1)/(x + 2)dx
- Q During the design phase of one of its model spacecraft, Spacez launches the Atlas 31415 rocket vertically. A camera is positioned 5000 ft from the launch pad. When the rocket...
- Q For the series problems, show ALL conditions required for the specified test for convergence or divergence.The Limit Comparison Test ?? ? 2/4n+1
- Q Jackson invested $590 in an account paying an interest rate of 61% compounded monthly. Ellie invested $590 in an account paying an interest rate of 61% compounded continuously. After 19...
- Q Gabriel invested $77,000 in an account paying an interest rate of 3 1/2% compounded monthly. Isabella invested $77,000 in an account paying an interest rate of 41/8% compounded quarterly. After...
- Q Its radius is 38 m. Find the circumference and area of the courtyard.Circumference:_________Area:________________
- Q Evaluate exactly:(a) log?27+ log?(b) In ?e=(c) 2e^ln2=
- Q Simplify as instructed.(1) sec(t) cos(t)= _________ Using sec(t) = 1 / cos(t)(2) = _________adding using common denominator(3) = ____________ Using sin(t) + cos (t) = 1
- Q Let h(x) = -9 - 2x.Use the limit definition of the derivative to differentiate h.h'(x) = _ ______________Determine the slope of h at x = 0.h'(0) =_______________
- Q Let g(x) = x + 3x +5Use the alternative limit definition of the derivative to determine the derivative (slope) of g at x = 2.g'(2) = _____________
- Q (1) Multiply. (1 + cos(t))(1 ? cos(t))= __________________(2) Simplify further using identitysin (t) + cos (t) - 1(1 + cos(t)) (1 - cos(t))= ___________
- Q For y = 6 cos(1/2)x(1) it's amplitude is __________(2) it's period is _________
- Q The following equation is_______ true.2sin(x)=??(A) Always(B) Never(C) Not enough information(D) SometimesThe following equation is_______ truecos(x) = ?3(A) Never(B) Sometimes(C) Always(D) Not enough information
- Q Let f(x) = {?x+1 if x<3{5- -x if x ? 3.Determine the one-sided limits as x approaches 3, and determine the limit as x approaches 3.
- Q Given x = t + 2t - 1 and y = t + 4t + 4, what is the equation of the tangent line at t = 1.
- Q Determine whether each of the following geometric series converges or diverges. If it converges, findits sum.(a)?^?n=1 36?/2?+(b) ?^?n=3 4?3-?-
- Q Of all points (x ,y ,z) that satisfy x + 4y + 3z=21, find the one that minimizes (x ? 1) + (y ? 1) + (z ? 1).The given...
- Q Solve for x:a) 3? = 9?b) 3-? = 4?c) log? (4x - 7) = 2d) log?(x + 3) + log?(2-x) = 1
- Q Of all the numbers whose sum is 20, find the two that have the maximum product.The two numbers whose sum is 20 and that have the maximum product are....Simplify your...
- Q Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum.f(x,y) = xy; 14x + y = 14There is a ________...
- Q Find and simplify the expression if f(x)=x-9f(4+h)-f(4)=_______
- Q Question 8Solve: log_3(9x + 17) log_3( 5x - 15)=2 x=_____ (Enter DNE if no solution exists)
- Q Prove the following propositions for all positive integers n.(a) 1+5+9+ 13 +...(4n - 3)=n(4n-2)/2(b)?k(k=1,n)=n(n+1)/2
- Q This problem has two parts.Part 1: Given that y = 4 sin(?), with ? (0,?/2), express each of the following as a function of y.cos(?)cos(?) cot(?) =tan(?) =
- Q (05.01, 5.05, 5.07 MC)Let ? = - (8?/3)Part A: What is a coterminal angle of ? such that 0 ? ? ? 2?? Part B: What are the exact values...
- Q Use the graph of f to find the indicated limit and function value.a. lim f(x) b. f(-2)a. Select the correct choice below and, if...
- Q Solve:(4x - 21)/ (x - 6) ? 3x ? ___________ (Enter your answer in INTERVAL notation, using U to indicate a union of intervals; or enter DNE if no solution...
- Q Use the equation for the function f(x) = x - 10 to find and graph the furtherFind f(x).f-(x) =_____
- Q Orange juice, a raisin bagel, and a cup of coffee from Billy's Breakfast Bar cost a total of $3.00. Billy posts a notice announcing that, effective the following week, the...
- Q In a recent year, companies spent a total of $89.6 billion on newspaper, television, and radio ads. The total amount spent on television and radio ads was only $3.2 billion...
- Q About 250,000 people of a certain community live in the country. Of that number, 73,910 live in state A and state B. The number of people of that community in...
- Q Solve:log_3 (9x + 17) - log_3(-5x - 15)X =_____ (Enter DNE if no solution exists)
- Q At low altitudes the altitude of a parachutist and time in the air are linearly related. A jump at 2,500 feet lasts 100 seconds.(A) Find a linear model relating altitude...
- Q A one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates....
- Q Suppose - 2x - 4x - 5 ? g(x) ? - 3 for all x-values near x = - 1, except possibly at x = ? 1.Use the Squeeze Theorem...
- Q Test the series for convergence or divergence:?? k=1 k!/1.4.7.........(3k+1) = 1!/1.4 + 2!/1.4.7 + 3!/1.4.7.10 + .................
- Q lim (?x + x)x->4[A] 4 [B] 4.472 [C] 20 [D] 18ABCD
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