Calculus question and answers for November 24, 2023
- Q Three different forces act on an object. They are:F?1< 2, ? 3 >2, 5 >< ?8, ? 5 >F?2F3=Find the net force Fnet on the object (the sum ofthe forces)FnetFAFind...
- Q Let h(t) =tan(2x + 3). Thenh' (1) isand h''(1) is
- Q Which pair of lines are parallel?a. x+7y-2=0, r = (2,5)+s(1,7), se R3x-4y-2=0, r = (1,4) +s(-3,4), s Rc. 2x+2y+2=0, r = (1,2) + s(1,-1), se Rb.ed.none of the above
- Q At a computer store, a customer is considering 6 different computers, 9 different monitors, 7 differentprinters and 4 different scanners. Assuming that each of the components is compatible with one...
- Q A man has 10 shirts and 3 ties. How many different shirt and tie arrangements can he wear?He can weardifferent shirt and tie arrangements.
- Q A true-false test consists of 5 questions.a) In how many ways can the test be completed, selecting true or false for each question?b) What is the probability that a test...
- Q The DNA molecule is a double helix consisting of two strands joined by bonds involving 4 substances called bases: adenine, cytosine, guanine, and thymine. Assume that these bases are uniformly...
- Q 6. The sum of two positive numbers is 16. What is the smallest possible value of the sumof their squares? The possible sum of the squares isshow your work below.
- Q Assume that certain types of identification numbers range from 00-00-000 to 77-77-777, where only the digits 0 through 7 are used. An identification number is randomly selected.a) What is the...
- Q Six fair six-sided dice are rolled. An outcome is an ordered sequence of 6 numbers between 1 and 6. For example, the sequence 1-1-1-1-4-3 is different from the sequence 4-1-3-1-1-1.a)...
- Q f(x)=?4x-5g(x) = 5x-1Find f-g and fg. Then, give their domains using interval notation.(f - g)(x) =Domain of f - g :(f*g)(x) =Domain of f*g :CD
- Q Find the 34th derivative of the function f(x) = cos(x).The answer is function
- Q f(x) = ?5x-3g(x)=x+4Find f+g and fg. Then, give their domains using interval notation.(f + g)(x) =Domain of f + g :(f.g)(x) =Domain of fig2
- Q Mr. Tappis doesn't like to wear the same outfit twice in a school year (yeah, right).'At the beginning of the year, he had 5 pairs of pants, 2 pairs of...
- Q Find the derivative of (x) = ?4?x 6-X4Type your answer without fractional or negative exponents. Use sqrt(x) for ?x.f'(x) =(Cvi
- Q Find the limit. (If the limit is infinite, enter 'oo' or '-00', as appropriate. If the limit does not otherwise exist, enter DNE.)x-8x+xx-x-x+6lim
- Q Find the following limit:2xlimI?7xAnswer:--38x + 21x - 7
- Q If the odds against E occurring are 3:5, then find P(E) and P(E').P(E)= (Simplify your answer.)P(E')= (Simplify your answer.)
- Q Suppose H (x)=7x-3.Find two functions fand g such that (fog)(x) = H (x).Neither function can be the identity function.(There may be more than one correct answer.)
- Q Solve for x, using the inverse trigonometric functions. 2 cos x = 1O x = 1/3O x = 1/?O x = 74Ox = n/6
- Q Suppose you deposit $1000 at 4% interest compounded continously. Find the average value of your accountduring the first 3 years.
- Q Evaluate the limit: limh?0(?5+h)-25h
- Q Which grid is used to graph polar equations?O Coordinate gridRectangular systemO Polar gridAll of the choices
- Q For the real-valued functions f(x) =x +4and g(x) = 4x-7, find the composition fog and specify its domain using interval notation.x + 3
- Q f(x) = 5x-4g(x) = ?2x+3Find f g and f-g. Then, give their domains using interval notation.
- Q 12.) (a) lim sin xX ? 0(b) lim1xsin x cos xcos x tan xx ? 0 tan x
- Q At one point, license plates in a certain state consisted of 5 letters (excluding I and O), followed by 2 numbers. Complete parts (a) through (e) below.a) How many plates...
- Q An ordered pair of a function is given as (x, y).coordinates to find the corresponding pair of its inverse.SwapO InvertSubtractAddthe x and y
- Q Q1. The Taylor polynomial of order 2 generated by a twice-differentiable function f(x) at x = ais called the quadratic approximation of f at x = a. Find the (a)...
- Q 4. y=-3+2 sin(x+)amplitude:a)b) period.c) graphing interval that will include one period:d) Range.-Basic function:-including vertical stretch/shrink and shift.e) graph all transformations starting with y=sin(x + = = = ), theny =...
- Q If f(x) = x + 10/3, find f-(x).Of(x) = x + 10/3Of(x) = x - 10O f-(x) = x - 10/3f(x) = x + 10
- Q The distance between [(3 - 2i) * (8 - 1)] and (9 + 2i) isO ?620O ?610O ?54?640
- Q Suppose that f(x) is a continuous function with f(2)= - 10 and f(6) = 10. Determine whichchoice best describes the following statement."f(x) = 0 for some x in the interval...
- Q Which of the following is a vector equation of the equation below:2+2 = 3-1-7Ox= -2-7ty = 1 + 3tOx=2+7ty = -1 -3tO[x,y] [2,-1] + [7.-3]O[x,y] = [-2,1] + [-7,3]
- Q Estimate the limit numerically or state that the limit does not exist (DNE):sin (9x)limx-0
- Q Find the limit of the transcendental function.9.) (a) lim sin 2x5?6(b) lim cotX? 2TIX
- Q fv-x+5g(x) = ?5x-3fFind f-g and Then, give their domains using interval notation.9
- Q For the real-valued functions f(x) = 4x + 1, and g(x)=?x-2, find the composition f g and specify its domain using interval notation.
- Q Suppose H (x)=(9-6x)4.Find two functions f and g such that (fog)(x) = H (x).Neither function can be the identity function.(There may be more than one correct answer.)f(x) = 0g(x) =...
- Q Given the equation y=8 sin(5(x-4))+2`The amplitude is: 8The period is: 2The horizontal shift is: 4The midline is: y = 2XOTunits to the Right
- Q The point A(3, 9) lies on the curvey=xIf Bis the point (x, x^2), find the slope of the secant line AB for the following valuesof x. Use all decimal places...
- Q 4.) Evaluate the given piecewise - defined function for the indicated values.f(x)=x + 1,-x + 4x,-X(a) Find: f(3)if x ? 1if x > 1(b) Find: f)(c) Find: f(3x + 2);X...
- Q Solve using the quadratic formula.03x9x - 5X =List your answers, separated by commas. Give exact answers or decimals accurate to at least 3decimal places.O10386832sPopesc
- Q In Exercises 17-22, find the sum of the first terms of the sequence.The sequence is either arithmetic or geometric.17. 2.5.8....: n=1018. 14. 8. 2.:=9123 321 ...:^= 1119.4.-2.1.20.6.-3.21. -1, 11,22.-2, 24,...:=124'121.......
- Q Find the remainder when x + 6x + 4x - 3 is divided by x - 2 using remaindertheorem.370-3745
- Q Which of the following is a scalar?a parachutist falling at 20 km/h downwardO a car travelling at 50 km/h to the easta man's mass of 88 kgJhrya child pulling a...
- Q .In a field PQRS, which is in the shape of atrapezium, PQ|| RS, PQ-58 m and RS-24 m. Atriangular flowerbed XQR is cut in such a waythat, the shape of...
- Q Solve sin (t)t=-7 cos(t) for all solutions 0 ? t < 2?Give your answers accurate to 2 decimal places, as a list separated by commas
- Q 1-Given a geometric sequence whose first term is 15 and common ratio is - 2,find the third term.-120-606011
- Q Use the limit Theorem to find the following limits, if they exists.5.) (a) lim (2x - 3x + 5x)X? 2(b) limX? 02xX3x
- Q Solve the equation: m + 12m = 0Answer: m =Write your answers as a list of integers or reduced fractions, with your answers separated by (a)comma(s). For example, if you...
- Q ) (a) limX? 2+-7x + 10X - 2(b) limX ? -5x + 8x + 15X + 3
- Q Let y = 2(x - 5)2 - 6.Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on...
- Q The conjugate of 2 + 3i isO3+2i2/312-3iO-2-3i
- Q Find x in the following equation.X=logbx + log(x-6) = log27
- Q Solve 12 cos (w) - 10 cos(w) + 2 = 0 for all solutions 0 <w< 2?W=Give your answers accurate to 2 decimal places, as a list separated by commas
- Q A polynomial or integer that is left over after one polynomial or integer isdivided by another polynomial or integer is calleddividenddivisorquotientremainder
- Q A website requires users to create a password that is 7 characters long. Each character can contain numbers, or symbols chosen from ? , #, and 1. The password does...
- Q The set of points (2et, t), where t is a real number, is the graph of y =Hint: Think inverse.12xe x01/1/20OexOnx-mIn x - In 2O2e1XIn x - In 2it
- Q Solve 6 cos(4x) = 3 for the smallest three positive solutions.Give your answers accurate to at least two decimal places, as a list separated by commas
- Q Find x in the following equation.log 10(x+1) - log 10 (x-1)= 1X=(Type a fraction or an integer. Simplify your answer.)
- Q Solve 7 sinT =(5?) = 2 for the four smallest positive solutionsGive your answers accurate to at least two decimal places, as a list separated by commas
- Q Glenn and Kim are members of a comedy troupe that has 9 members in all. How many ways can the 9 members line up if Glenn and Kim must stand...
- Q Solve the equation 12y - 17y + 6 = 0.Answer: y =Write your answers as a list of integers or reduced fractions, with your answers separated by (a)comma(s). For example,...
- Q The engines of a plane are pushing itdue north at a rate of 300 mph, andthe wind is pushing the plane 20?west of north at a rate of 40 mph.What...
- Q Let f(t)= (1+t, 3, t, 7)||. What is the minimum value of this function of ?Answer the same question for the function g defined by g(t)= ||(1,3,7-t)ll.(10%)
- Q Solve the equation: x = - 17x - 60Answer: x =Write your answers as a list of integers or reduced fractions, with your answers separated by (a)comma(s). For example, if...
- Q Let f(x) = xDetermine the equation of the tangent line to f at x =12. Report the solution using slope-intercept form.
- Q Consider the quadratic function `f(x) = x^2-2x-8.Determine the following:The smallest x-intercept is `x = `The largest x-intercept is `x =The y-intercept is `y =
- Q Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.lim (cos(x))/
- Q Solve 12 sin(x) 13 sin(x) + 3 = 0 for all solutions 0 < x < 2?C=
- Q Let g(y) = -6y + 4Determine the derivative of g.g'(y)
- Q (x - 7/7) in terms of sin(x) and cos(x).6Rewrite sinx
- Q A pedestrian walks 7.4 kilometers westand then 9.2 kilometers south.What is the angle of thepedestrian's resultant vector?Hint: Draw a vector diagram.[?]
- Q Consider the number of fish, y, in a certain population.dydtThe annual rate of change of a fish population is given byWhat is the meaning of 0.1y in this differential equation?=...
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