Calculus question and answers for August 04, 2023
- Q Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)?1/x-4 dx
- Q Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form.?(18r^8 dr) / (?(4 - r^9), u = 4 - r^9.
- Q Evaluate the following integrals.(a)?4x + 1/ (x-2)(x - 3)dx(b)??x ln(?x) dx(c) x?+x+1/x + 2 dx2. Let I be the region bounded by the curves y=x, y = 1-x.(a) Give a...
- Q Suppose the field has a length of 25,000 feet. You buy fencing to enclose it, but discover you've bought 10 feet too much. Rather than throwing away the extra fencing,...
- Q A maintenance worker fills a swimming pool with water at a rate of 10m^3/minute.Suppose at t = 0, the swimming pool is filled with 100 m of water.How much water...
- Q Ken flies a drone in a circular path around an object that is 210 feet west and 190 feet north of his position.The drone's path takes it over a point...
- Q Evaluate the expression cos^-1(sin(4?/3))________________Give your answer as an exact value
- Q Suppose cos ? = 3/4Find the following.cos(- ?) =cos (180 - ?) =cos(180 + ?) =
- Q Let f(x) = x - 2x - 2 for all x ? 3The graph of f is given belowDetermine the following function value . Enter DNE if the function is...
- Q Find the length of an are of a circle of radius 18 feet intercepted by a central angle of 120.
- Q The lines r = (2, 1, 1) + p(4, 0, -1), p? R, and q = (3,?1, 1) + q(9, ?2, ?2), q? R, intersect at the point A.Determine the...
- Q Read and understand the problem, then solve. Stating what is asked in the problem. During the Apollo 14 mission, Alan Shepard hit a golf ball on the Moon. The function...
- Q What is wrong with the equation?-2? 1 x^(-4)dx=(x^(-3)/(-3))| =-3/8
- Q The graph of g is given below.Determine the intervals on which g is continuous. Enter the solution using interval notation.g is continuous on _____
- Q U xx + U yy = 2x, 0 < x < 1, 0 < y < 1u(x,0) = 0, u(1, y) = 0u(x,0) = 0, u(x, 1) = 0Solve your...
- Q Given that cos? = 5/13 and that ? lies in Quadrant IV, what is the exact value of sin 2??A) 120 / 169B) 24 / 13C) -(24 / 13)D) -(...
- Q Which of the following shows the simplified form of sinx/(1-cosx)?a)1b) sin x + tan xc) sin x + cot xd) csc x + cot x
- Q (This problem is similar to the example in your textbook about guessing a formula for the derivative of f(x) = x and to a similar problem in the exercises. Study...
- Q Solve the following system of equations.3x+5y-5z-21-4x=5z+172x-5y+6z=-16
- Q Using the shift or stretch theorem find the Fourier transform of {1 for 2 ? t ?0b(t)= { 0, otherwisegiven...
- Q Use the graph of f(x) given below to draw the graph of the function y = f(x + 3) - 2. Explain in words the changes in the graph.
- Q Now let's write down an iterated double integral that is equal to ? e?(x + y) dA in polar coordinates in the dA = r dr d? order.
- Q Find two solutions of the equation. Give exact answers in radians in the interval [0,2?].sin(t)=-(3^1/2)/2
- Q Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 405sin(405) = ______cos(405) = ______tan(405) = ______
- Q Convert the degree measure to radian measure as a multiple of and as a decimal accurate to three decimal places. (-480)multiple of ? = ____decimal = ____
- Q Solve the following equation for over the interval [0, 2?), giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as...
- Q Given functions m(x) = ?x+12 and p(x) = x - 5, state the domains of the following functions using interval notation.Domain of m(x)/p(x):Domain of m(p(x)) :Domain of p(m(x)) :
- Q Evaluate ? {(9x + 25) /x +( 6x +9)} dx using the method of Partial Fractions.
- Q Note: Triangle may not be drawn to scale.If ? B = 86 and a = 22, thenReport lengths accurate to 4 decimal places.Question for thought: Can you obtain the final...
- Q Ice Cream Sundaes. An ice cream shop has a choice of ten toppings.Suppose you can afford at most four toppings. How many different types of ice cream sundaes can you...
- Q Is 1800 coterminal with -1800? (a) Yes (b) No
- Q The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following function. The revenue from 115 gadgets is $37,271.-2/3 MR(x) = 4x (=...
- Q Let f(x) = log3(x-4).a. Use transformations to graph the function.b. Write the domain and range in interval notation.c. Determine the vertical asymptote.
- Q Evaluate the double integral for the function f(x, y) and the given region R.f(x, y) = y e^x^; R is bounded by x =y/6, x = 1 and y =...
- Q ?1-tanx1+tanx dx
- Q f and g are functions of x and y. f(1,2)= 2 and g(1,2)= 1. Also at (1,2)df = -2dx + 5dydg = 4dx - 3dyz is a function of (x,y)...
- Q Use Green's Theorem to evaluate the line integral along the given positiveley oriented curve:?xy dx - 3y dy, C is the circle x + y = 1
- Q Solve the equation for x.log (x+16) = log (x) + log (4)x=__
- Q (a) Evaluate the following indefinite integrals. Show complete working. In particular: if you use substitution, write down the substitution that you used. Show the full working needed to make that...
- Q Using the diagram on the right, choose the best estimate for the central angle in degrees.a) 263c) 283b) 273d) 293
- Q Which x-value is in the domain of the function f (x) = 3cot(4x) + 2?
- Q Two fair six-sided dice are rolled. Let A = the event that the dice add to 8, and let C = the event that the dice show the same number....
- Q Solve by addition.7x - 2y = 34x + 5y = 3.25
- Q Find the slope of the graph of f(x) = ?x whena) x = -1b) x = 2c) x = 0
- Q Given the vector field F(x, y) = (x, xy, xyz) and the oriented line segment C from (1,1,1) to (2,1,0), compute c?F. dr.
- Q The terminal side of an angle 8 in standard position intersects the unit circle at(-12/13,-5/13)What is sin (?)?Write your answer in simplified, rationalized form.
- Q Solve the following equation by the quadratic formula below.36x + 7x-6=0Give the answers in ascending order. Round your answers to three significant digits.x1 -0.51688x2= 0.32244
- Q Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm/s) is the areacm/s
- Q Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.1) f(x) = x2 between x = 4 and x...
- Q f(x) = x between x = 0 and x = 4 using an upper sum with two rectangles of equal width.
- Q Find the total area of the region between the curve and the x-axis.y=1/?x; 1?x? 4
- Q Use the given transformation to evaluate the integral.??3x dA, where R is the region bounded by the ellipse 9x^2 + 25y^2 = 225; x = 5u, y = 3v
- Q Solve the following equation.x^2/3 - 5x^1/3+6=Larger x=Smaller x=
- Q Evaluate the integral by making an appropriate change of variables.?? 3 cos (9 (y-x / y+x)) dA where R is the trapezoidal region with vertices (8, 0), (10, 0), (0,...
- Q Find the area of the finite part of the paraboloid y = x + z cut off by the plane y = 81. [Hint: Project the surface onto the xz-plane.]
- Q Stock Prices The weekly closing price of a corporation's stock in week t is approximated byf(t) = 70+ 4t cos(?t 6) (0 ? t ? 15)where f(t) is the price...
- Q Find the power series expansions for the following functions and specify for which x-values the expansion is valid.(a) f(x) 1 xHint: Rewrite 1 x = 1 1 - (1 -...
- Q Solve the equation. Enter the solution below.3x - 1 = 25
- Q Use the calculator to find the following. Round your answer to 4 decimal places.In 7
- Q Solve the following system of equations.2a - 20b = 04a + 70c = 5040b + 56c = 42Select the correct choice below and, if necessary, fill in the answer box...
- Q Let g'(y) =- 2yFind the particular solution to the above differential equation that satisfies the following initial condition.g(6) =-8g(y)=
- Q For the real-valued functions f(x) = x-4 x+1 and g(x) = 4x-5, find the composition fog and specify its domain using interval notation.
- Q Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)F"(x) = 32x - 18x + 10xf(x) =
- Q A particle is moving with the given data. Find the position of the particle.v(t) = sin(t) - cos(t), s(0) = 5s(t) =
- Q Use the formula A = P(1+ r n)nt.Kendra invests $5800 in an account that earns 5.2% annual interest compounded quarterly. How much will be in the account after 5 years?...
- Q A farmer wants to fence in a rectangular pict of land adjacent to the north wall of his bar. No fencing is needed along the barn, and the fencing along...
- Q Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0).smaller y-value (x, y) =larger y-value (x, y) =
- Q A retailer has been selling 2000 tablet computers a week at $350 each. The marketing department estimates that an additional 80 tablets will sell each week for every $10 that...
- Q Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)arctan(x) = x2 4
- Q Solve the system of equations. You may use any method of your choice, but your method must be algebraic (not graphical). If the system is inconsistent, state there are no...
- Q The owner of a ranch has 6000 square yards of fencing to enclose grazing land that is subdivided it into 3 parts by means of fences running parallel to the...
- Q A defense contractor is starting production on a new missile control system. On the basis of data collected during the assembly of the first 16 control systems, the production manager...
- Q Find the function with the given derivative whose graph passes through the point P.g'(x) = 2 x3 + 20x4, P(1,6)
- Q Let h(z) = (z + 4) (z ? 5)Determine the most general antiderivative of h.?(z + 4) (z ? 5)dz =
- Q Use logarithms to solve the equation symbolically.Inx+ Inx2 = 6
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