Calculus question and answers for January 07, 2024
- Q 2 For each of the functions below use your graphing calculator to draw a graph of the function and then estimate the x coordinates of its inflection points List all...
- Q 6 Use the graph of y g x below to estimate point s of inflection for the function g x as well as the intervals on which g x is...
- Q 7 Suppose you know that f x is an odd function on the domain of all real numbers and that th function is concave up on the intervals 0 x...
- Q 3 Consider the function f x 2x 3x 6 x 2 A Find f x Show your work B Graph f x on your calculator and use this graph to...
- Q 4 Consider the function x x x 3 x2 As in the last problem find f x showing all work and use the graph of this function to estimate where...
- Q 2 Consider the function f x x x Use graphical methods to discuss the differentiability of the function In particular find all values of x for which the function appears...
- Q Find a power series solution of the form y x 0 Cnx of the given differential equation x y y 0 First compute y x Use cn for c in...
- Q Find the power series solution of the initial value problem Assume the form y x 0 Cnx n 0 y x n 1 Then compute n C x 1 0...
- Q 3 Consider the function f x 1 x4 5x 4 Use graphical methods to discuss the differentiability of the function In particular find all values of x for which the...
- Q Find a power series solution Cnx of the given differential equation Determine the radius of convergence of the resulting series and by comparing with a table of well known series...
- Q 6 Below is a graph of the curve y 10 1 50sinx C x 3 10 Looking at the graph it s clear that the function has three zeros in...
- Q 1 Below is a graph of the function y f x 5 From your observations of this graph state with reasons the values of x at which fis not differentiable...
- Q Find the recurrence relation for the coefficients of the power series solution of the differential equation y y 2y 0 Assume the form y x 0 Cnx in y x...
- Q 6 Below is the graph of y g x 17 0 4 I Note The open circles at x 2 are to imply that the function g is not defined...
- Q x2 2x 1 2x3 3x 3x 1x4 x 9x 24 if 4 x Discuss the continuity and differentiability of the function at x 1 and x 4 Prove your assertions...
- Q 1 point For the system of differential equations x t x y 2xy 20 y t 8x 2y xy the critical point xo yo with xo 0 yo 0 is...
- Q 1 point Find the eigenvalues and corresponding eigenvectors for the matrix P A V saddle center point ellipses spiral source spiral sink none of these 28 12 6 12 and...
- Q a Find the eigenvalues and corresponding eigenvectors for the matrix P A x t x 1 V 17 20 15 18 and A 11 E b Find the most general...
- Q 5 Below is a graph of the curve y 4x cosx 10 10T SIX 10 Your friend claims that the slope of the tangent line to the curve at x...
- Q 13 Find the limit of the sequence if it converges otherwise indicate divergence 2 2 n an 14 Find the limit of the sequence if it converges otherwise indicate divergence...
- Q Now take a look at the following three functions f x x 2x 1 500 g x x 0 X k x x 21 For each function do the following...
- Q 1 Find the slope of the tangent line to the curve y x3 2x 1 at the point 1 0 Find the equation of that tangent line On your calculator...
- Q 3 Below is a graph of the curve y 10 5 15 10 5 0 10 cosx sinx 1 2x2 I 3 10
- Q 4 Here is a graph of the curve y x3 5x 4x 101 I Your friend tells you that the slope of the tangent line to the curve at x...
- Q Earth s distance from the center of the sun as a function of time 1 Point
- Q Find the amplitude phase shift and period of the function y 1 2 cos 2x 2 Give the exact values not decimal approximations Amplitude 1 Phase shift 3 X B
- Q 7 Use a half angle formula to find the exact value of tan 8 tan 7z 8 2 16
- Q 37 If f x sec x then lim X A 0 B sec C sec tan 5 D nonexistent 15 00 f x f 5 T X 3 is
- Q 4 Suppose f x if x 2 x 3 if 2 x Identify any points of discontinuity and determine giving reasons if they are removab infinite essential or jump discontinuities...
- Q A First class postage as a function of weight 1 Point
- Q B Atmospheric pressure as a function of altitude 1 Point
- Q 1 Given f x x 17 identify any points of discontinuity and determine giving reasons if 6x x 1 they are removable infinite essential or jump discontinuities 2 Points
- Q x3 2x 2 x ax b 4x4 3x 5x 2 if 1 x find values for a and b so that the function is continuous for all x 4 Points...
- Q 5 Find all the constants a that make the function f x 3 a x if x 3 a x if x 3 continuous for all x 2 Points
- Q C Average daily temperature as a function of the day of the year 1 Point
- Q 3 Suppose f x sin x2 4 1 Identify any points of discontinuity and determine giving reasons if they are removable infinite essential or jump discontinuities 3 Points
- Q Consider the system 8 238 E nd the solution curve passing through x y 1 0 and write it in th m F x y 0
- Q Sally s anime club is selling brownies to raise money Instead of just aiming blindly Sally does some market research to try and maximize the club s prom E 4p2...
- Q C Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem Total Cost for Electrician Services 330 900...
- Q Khalil Problem 4 3 Consider the system x x 1 x x x x 1 x x Use a quadratic Lyapunov function to show that the origin is asymptotically sta
- Q The weight in pounds of a newborn baby t months after birth can be modeled by W A graph of W is shown below Write an equation for W then...
- Q Given z 2 xy x uv w y u ve z du then find 20 043 when u 1 v 3 w 0
- Q a c Use the criteria indicated to create a pair of 3 x 3 matrices D D where the entries of the matrix D are all integers 20 marks i...
- Q b Let f R R be a function and suppose ff t dt a Show that x y z b y 2 where D is the unit ball x y...
- Q f x 20x3 12x2 6 f 0 3 f 1 0 find f
- Q Solve the following boundary value problem Ytt 25yxx 0 x 4 t 0 y 0 t y 4 t 0 y x 0 0 y x 0 x 4 x...
- Q 3 The int operator in your calculator is the greatest integer function It returns the greatest integer less than or equal to the operand and is written using square brackets...
- Q The number of times a new pop song has been downloaded t weeks after its initial release is given by f t a After how many weeks is the rate...
- Q x b Given the function g x cos x that will make the function differentiable A 0 B 1 C 2 D No such value exists x 0 x 0...
- Q 4 The domain of f x is 0 and 1 2 3 4 1 17 X f x 1 12 1 2 5 10 10 A Find an equation for...
- Q If f x sin 7 5x find f 7 O A 0 657 OB 0 754 O C 0 OD 0 657 OE 3 770
- Q Which of the following functions is continuous but not differentiable at x 1 x x 1 2x x 1 I y x 1 II y III y x x 1...
- Q The derivative of y 1 sin x COS X is O A tan x O B O C O D O E 1 1 sin x sin x COS X...
- Q The slope of the tangent line to the graph y x at the point 1 is A 1 B 0 C 2 D 1 3 E Undefined
- Q Suppose the functions fand g and their derivatives have the following values at x 1 and x 2 Let h x f g x Evaluate 1 A 6T B 24...
- Q The inflection point of the curve y 8x 24x 7x 3 is O A 1 23 OB 0 3 O C 1 21 OD 2 59 OE There is no...
- Q If g x tan 5x2 then g x O A 10xsec 5x tan 5x OB C 7xsec 5x 10xsec 5x OD 10sec 5x2 O E sec 5x O O
- Q Suppose a company s revenue function is given by R q q 390g and its cost function is given by C q 350 12g where g is hundreds of units...
- Q What is the value of g 0 if y g x has a graph given by 2 1 10 OA O OB 4 O C 3 O D 1 OE...
- Q Assume the function f is defined as f x 5cosx 4sinx Use the corresponding derivative rules to find the second derivative f x and evaluate that second derivative at x...
- Q Assume the function f is defined as f x 5 cos x 4 sin x Use the corresponding derivative rules to find the second derivative f x and evaluate that...
- Q Find the derivative of the given function dx 3 y 8 cos x
- Q Find the derivative of the given function 3 y 5 log x dy 11 Type an exact answer
- Q Find the derivative of the given function V 20 tan s 1 dV ds Type an exact answer using radicals as needed
- Q Find the differential of the function y The differential is dx 12eX X 7
- Q Find the derivative of the given function 2 y 3 sin x sec x Choose the correct answer below O A O B O C O D dy 6 sec...
- Q Evaluate the limit if it exists Use L Hospital s rule if appropriate lim X 0 lim x 0 In cos 4x 3x In cos 4x 3x Simplify your answer
- Q Find the derivative of the given function r sin 30 dr Type an exact answer using a pooded
- Q Find the derivative of the given function y 3 sin 6x dy dx 0
- Q Find the derivative of the function by using the product rule Then multiply out the function and find the derivative by treating the function as a polynomial Compare the results...
- Q Find the derivative of the function Do not find the product before finding the derivative y 4x 3x5 5x Choose the correct answer below OA y 4x 15x4 10x 3x5...
- Q Find all the higher derivatives of the following function y 6x 4x dy dx d y 2 dx 11 18x 8x
- Q Find the derivative dy y 4 24x 2
- Q Find the second derivative f x 5x 3
- Q Find the derivative of the given function y 3sin 3x4 5 dx
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