Calculus question and answers for January 11, 2024
- Q The position of a particle moving in a straight line is given by s t et cos 5t for t 0 where tis in seconds If the particle changes direction...
- Q Find the domain of the function f x x 2 A x22 C no solutions B x 2 D x 2
- Q For what values does the function fail to exist A x 5 and x 0 f x C x 1 5 and x 0 X x2 5x B x 0...
- Q For this question refer to the following graph and information An ant is crawling on a straight wire The VELOCITY v t of the ant at time 0 t 8...
- Q da O A O O B O c x 3 x ln 2 1 3x O D None of the above 1 O E x In 2
- Q Find a definite integral for which 1 4 4 k 4 4 4 is a right rectangle approximation 5 O A x dx B x 4x dx c x 4x...
- Q dx O A OB B e3r 1 e z 1 2 2 1 e 1 x 1 2 O c 1 1 2 O D 3 D 2 1 2...
- Q dr VI dx evit got O A O B 3r e 1 e x 2 e r 2 1 e r 1 2 OC 1 1 2 c O D...
- Q The average value of v t et cos t over the domain 1 4 is approximately OA 2 840 105 OB 2 516 x 105 O C 1 149 x...
- Q If fis continuous for all x which of the following integrals necessarily have the same value cb a f x dxII f x a da III cb 1 f x...
- Q f x ln 3x 36 Then f x 24x O A 3 36 OB O C O D 12x In 3x 36 3 x 36 12x 37 36 2 ln...
- Q dlog5 x 1 dx O A OB B O C Hol O D 1 2 x 1 In 5 2 2 1 In 5 x 2 x 1 X D...
- Q y g x on 3 4 is given by the following curve which is composed of two line segments and a semicircle Click here for long description Evaluate f3 g...
- Q The function g x 12x sin x is the first derivative of f x If f 0 2 what is the value of f 2 O A 2 5 OB...
- Q Solving the equation 16 x OA x 3 5 OB X 2 23607 OC x 1 or x 2 OD x 2 7182818 OE None of the above you get...
- Q Suppose f x 9 x Then on any interval where the inverse function y f x exists d x dx OA 2x 1 B 9 x 1 2 O c...
- Q Which of the following ould represent an y f x A b where b 1 I II III 2 40T A I only B II only C III only D...
- Q For all positive x log log4 a Hint Think change of base O A log4 x log x B log4 2 1 2 O c log4 x O D log24...
- Q Consider the following graph of y 10 8 6 4 O A I only OB II only O C III only 2 D Both I and III 10 5 0...
- Q 1 Which of the following will give the smallest value for da for a given number of intervals A A right hand Riemann sum approximation B A trapezoid approximation OC...
- Q The region Ris bounded by the x axis x 2 and y x Which of these expressions represents the volume of the solid formed by revolving R about the line...
- Q Suppose f x sin cos x On any interval where the inverse function y f x exists the derivative of f x with respect to x is OA B C...
- Q What is the area bounded by y x and y 3x A 5 OB 8 O C OD 25 OE 11 2 72
- Q If f 3x x 1dx udu then So S a A a 2 b 4 OB a 8 b 64 OC a 12 b 48 OD a 7 b 63...
- Q 4 If f 3x x 1dx udu then 2 a O O A a 2 b 4 B a 8 b 64 C a 12 b 48 OD a 7...
- Q Consider the function f x 100 of the following are true I lim f x 70 XIX II lim f x 70 118 III lim f x 100 18 IV...
- Q Suppose y f x 3x 5 Then the inverse function f x 3 A 2 5 3 OB 5 5 O c 5 3 O D 3y 5 E 3x...
- Q Which of the following statements is true I 3 3 II 24 48 812 III 3 9 2 33x 4 OA I only OB II only OC Ill only OD...
- Q Suppose that y f x x 4x 4 Then on any interval where the inverse function y f x exists the derivative of y f x with respect to x...
- Q Suppose f x Find the slope of the tangent line to the graph of y f x at 3 1 You get OA 972 1 O B 24 C 00062...
- Q Suppose x 4x f Find the slope of the tangent line to the graph of y f x at 3 1 You get OA 972 1 OB 24 C 00062...
- Q A mass suspended from a spring is raised a distance of 5 cm above its resting position The mass is released at time t 0 and allowed to oscillate After...
- Q An isotope of sodium has a half life of 20 hours Suppose an initial sample of this isotope has mass 10 grams The amount of the isotope in grams remaining...
- Q Suppose that y f x 2x x 0 Find a c 0 such that the tangent line to the curve y f x at x chas the same slope as...
- Q Suppose 4 O O O O A In 12 OB 3 O c log4 12 OD log12 2 O E 12 en x
- Q Suppose that f x is an invertible function that is has an inverse function and that the slope of the tangent line to the curve y f x at the...
- Q X F where F ri yj and S is the curved portion of the right circular cone given by 2 y 2 0 0 1 Hide Transcribed Text b Calculate...
- Q Solving the equation 33x 235 2 for x you get x O A 17 O B log3 5 O c log3 5 OD 7 O E 35
- Q f x x x 18x 4 Over which of these domains could you define f x Remember that f x must be one to one only one y value for...
- Q Let f x x 3 2 The graph of the inverse function y f x has a vertical tangent at HINT Think about the symmetry of the 2 graphs O...
- Q Graph the function f x over the given interval Partition the interval into four subintervals of equal length Then add to your sketch the rectangles associated with the Riemann sum...
- Q 4 k 1 Graph the function f x over the given interval Partition the interval into four subintervals of equal length Then add to your sketch the rectangles associated with...
- Q 4 Graph the function f x over the given interval Partition the interval into four subintervals of equal length Then add to your sketch the rectangles associated with the Riemann...
- Q b g b Use the Substitution Formula ff g x g x dx f u du where g x u to evaluate the following integrals g a a y 1...
- Q Which of the following expresses 1 3 9 27 81 243 729 in sigma notation 7 a 3k 1 k 1 6 b 3k k 0 5 c 3k 1...
- Q Find the volume of the following solids The base of a solid is the region between the curve y 8 sin x and the interval 0 on the x axis...
- Q Find the derivative of the given function r t tan 2 5t 11
- Q Suppose that x and y are related by the equation 4x y 4 and use implicit differentiation to determine dy dx dy
- Q Find the derivative of the given function y 8sin 4x 7 dy dx II
- Q Linearize f x 4 x for a 3 and use it to approximate the value of 1 8 x
- Q Find the derivative of the given function R T7e T dR dT
- Q Find the derivative of the given function y 6sin 5x 4 dy dx
- Q Find the derivative of the given functio 7x 6 x dy y In
- Q Suppose that x and y are related by the equation 4x 3y 3 and use implicit differentiation to determine dx dy dy 11
- Q Differentiate the function dy dy y 1 3x 1 5
- Q Find the derivative of the following function 5x 8 f x f x 2 x 4x 9
- Q 8 points EACH part Verify the Divergence Theorem is true for the vector field F x y z xi y j zk and t surface S is the plane 2x...
- Q Measurements of a lake s width were taken at 15 foot intervals as show 0 f x 0 Estimate 120 If x dx f x dx with n 4 using...
- Q 2x 1 2 Let be the function shown below with domain the closed interval 0 6 The graph of f is shown below composed of two semicircles Let h x...
- Q 3 The base of a solid is a right triangle whose base side has length a and whose perpendicular side has length a Find the volume of the solid if...
- Q The domain of the function f x arccos 3x2 2 is O A all x in the interval 1 3 U 1 OB all x in the interval 0 1...
- Q Glenn is 35 feet from the base of a rocket looking up at the tip of its nose cone which is 80 feet higher than the level of Glenn s...
- Q Consider the function f x x 4x 5 x 2 You have that f x 1 O A where x and y are related by the equation y x 4x...
- Q A tetrahedron has three mutually perpendicular faces and three mutually perpendicular edges of lengths 2 3 and 4 cm respectively Find its volume
- Q x 2 The base of a solid is a region bounded by the curve 82 18 1 an ellipse with the major and minor axes of lengths 16 and 8...
- Q 4 A solid has as its base the region bounded by the curves y 21 2 and y x 1 Find the volume of the solid if every cross section...
- Q 1 Consider the region bounded by the graphs of x y2 and x 9 Find the volume of the solld that has this region as its base if every cross...
- Q You ll be working with the function y f x x 1 5 2 and the interval you ll always be concerned about is 2 6 Here s a graph...
- Q A Find the equation of the normal line to the curve In y3 2x 1 at the point 1 1 I
- Q Use the appropriate Product Rule to evaluate the derivative where ri t 9t 3 t r t 6 e 4 dt r t r t 54 3e 8t Answers Attempt...
- Q 4 A certain computer algorithm used to solve very complicated differential equations uses an iterative method That is the algorithm solves the problem the first time very approximately and then...
- Q 2 Two separate rabbit populations are observed for 80 weeks starting at the same time and with the same initial populations The growth rates of two rabbit populations are modeled...
- Q Evaluate dr g t using the Chain Rule r t et est 8 g t 3t 6 r g t 9
- Q Find a parameterization for the circle of radius 4 in the xy plane centered at the origin clockwise r t y t z t 9
- Q Let r t t 4 i Then lim r t t 1 t 4 t 2 j sin 3 t k i Ij
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