Calculus question and answers for February 08, 2024
- Q Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or or x48
- Q Suppose f 2 8 f 2 9 g 2 3 g 2 1 and that f x g x are continuous for all x f x 8 lim x2 g...
- Q Evaluate the limit using L H pital s rule 7x lim X18 e5x
- Q Question 12 Evaluate lim sin 9x o A
- Q Quest no Evaluate the limit using L H pital s rule X e 2x 1 6x lim x 0
- Q Question 4 lim x 0 Evaluate the limit using L Hospital s rule 4 5 X
- Q The lesser til is a zentiplicity so the graph on OA o OA d Use a graphing utility to graph the function The graphs are shown in the viewing window...
- Q e Approximate the turning points of the graph The turning point s of the graph is are 3 16 34 33 5 16 6 90 Type an ordered pair Round...
- Q Analyze the polynomial function f x 3 x 3 x 4 using parts a through h below The graph of f behaves like y 3x for large values of x...
- Q 3 If the price charged for a candy bar is p x cents then x thousand candy bars will be sold in a certain city where p x 149 2...
- Q Find the domain and range for the quadratic function with a vertex 10 0 if the graph opens down help intervals Domain M Range help intervals
- Q Rewrite the quadratic function f x 5x 10x 9 in standard form f x a x h k and give the vertex help numbers f x Vertex help points
- Q ind the general form of the quadratic function with the vertex 3 2 and a point on the graph 5 6 f x help formulas
- Q Find the general form of the quadratic function that has a vertex of 2 2 and a point on the graph 5 51 f x help formulas
- Q Rewrite the quadratic function f x x 8x 3 in standard form f x a x h k and give the vertex help numbers f x Vertex Ex Quadratic Function...
- Q For the quadratic function f x x 4x 5 find the vertex the axis of symmetry and the x intercept s Express the vertex as a coordinate pair If there...
- Q Determine whether f x 4x 16x 4 has a minimum or maximum value and find the value of the minimum or maximum Also find the axis of symmetry The y...
- Q Determine the domain and range of f x 7 x 5 3 Enter the solution in interval notation help intervals Domain Range help intervals
- Q C f x x 0 16 Graph the function the secant line through the endpoints and the tangent line at c f c y y 5 15 10 5 y...
- Q 13 3 Analyze the polynomial function f x x x 7x 21 Answer parts a through h 24 8 8 3 4 8 8 e Approximate the turning points of...
- Q Let f x x 3 2 Find all values of c in 1 4 such that f 4 f 1 f c 4 1 Enter your answers as a comma...
- Q For the polynomial function f x 8x x 2 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the...
- Q 8 A town with a population of 100 people grows to a population of 200 in five years Assume the dP population P grows exponentially according to the equation kP...
- Q Follow the instructions in each problem Show supporting work not just a final answer to receive cre 1 Compute the second derivative d dx2 218
- Q 7 Compute the derivative of f x 2 en r
- Q 4 Find the derivative of f x cos x Note you do not need to simplify your answer
- Q 2 Compute the derivative for the function y x e dy dx Note you do not need to simplify your answer
- Q 6 Compute the derivative of y ln x 5
- Q 5 When 2x xy 4y 2 express dy in terms of x and y using implicit differentiation dx
- Q Analyze the polynomial function The y intercept s is are 21 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each...
- Q The radius of a sphere is increasing at a rate of 3 mm s How fast is the volume increasing when the diameter is 80 mm mm s
- Q R If two resistors with resistances R and R are connected in parallel as in the figure below then the total resistance R measured in ohms 22 is given by...
- Q Each side of a square is increasing at a rate of 2 cm s At what rate is the area of the square increasing when the area of the square...
- Q h x 2x 15x 144x 1 Given the function above use the First Derivative Test to find the local extrema Select the correct answer below There is a local maximum...
- Q The line y 5 is a horizontal asymptote to the graph of which of the following functi sin 5x y B y 5x C y 5x D 1 x 1...
- Q 31 02 03 04 1 5 25 Lt fbe the function given by f x 1 2 2 x 20 D nonexistent the line yb is a borineal asympaote to...
- Q Graph of 18 The graph of a function is shown above Which of the following limits does not exist E lim f x A lim f x B im f...
- Q B 2 16 C 3 D nonexistent If f is a continuous function such that f 2 6 which of the following statements must be A lim 2x 3 B...
- Q 1 Is the function f x continuous at x 27 Give a reason for your answer t hrs v t miy hr 1 2 4 5 7 3 8 6...
- Q A 2 19 2mx for x 2 i 11 Let be the function defined above where e is a constant If f is continuous at x 1 what is the...
- Q et x 0 Find y using implicit differentiation if xy y 1 0
- Q Here is the graph of a quadratic function f 5 0 12 10 5 0 2 0 5 4 4 Of x x 4 4 5 6 0 Select all...
- Q 8 The graph below shows the first derivative of a function y f x Select a possible graph of f that passes through the point P A C f M...
- Q 1 From a thin piece of cardboard 30 in by 30 in square corners are cut out so that the sides can be folded up to make a box What...
- Q An explanation of Rolle s Theorem How is it a special case of the MVT o What can it tell us about the location of critical point s o What...
- Q Question 3 20 points 3 Find the derivatives of the given functions a 2x 1 x y ln b In 2x In 1 x 3x y e x cos 4x
- Q 1 Find the derivatives of the given functions a y 2 sin 2x 1 b y 3 cos 5x 2
- Q In 2000 the birthrate in a certain area increased from 16e0 02t million births per year to 21e0 02t million births per year where it is the number of years...
- Q Verify the identity tan u sin u tan u sin u sin u tan u sin u 11 E sin u cos u sin u cos u cos u sin...
- Q Prove the identity tan x 1 tan x 3 1 3 tan x 1 3 tan x tan x tan F 3 tan x 3 1 3 tan x 3...
- Q Find the area bounded by the given curves y 4x 1 and y 4x 1
- Q Math 126 Homework 15 2 12 pts Find all zeros real and non real Completely factor the polynomial into a polynomial with linear factors q x 4x 20xXx 4x 13
- Q A polynomial P is given P x x 81 a Find all zeros of P real and complex Enter your answers as a comma separated list Enter all answers including...
- Q a If a is a zero of the polynomial P x then b If a is a zero of multiplicity m of the polynomial P x then must be a...
- Q Prove the identity tan x tan x Use the Subtraction Formula for Tangent and then simplify tan x tan tan x 1 tan x x tan x 0 1 tan...
- Q Verify the identity sin 8 tan 8 Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine and then simplif sin 8 sin 8 tan 8...
- Q Simplify the trigonometric expression sec x 1 sec x 84 222
- Q Prove the identity sin x sin x Use the Subtraction Formula for Sine and then simplify sin x 1 sin x sin x 1 cos x sin T Cos x...
- Q Prove the identity sin x 7 cos x 2 Use the Subtraction Formula for Sine and then simplify sin x sin x cos cos x CO sin x 0 cos...
- Q Intervals of Concavity and Points of Inflection Answer the following questions using the function f x 4x 2x 4 1 z f has points of inflection that occur at NOTE...
- Q Find the area between the curves y ex and y e x shown below from x 0 to x 1 Leave the answer in its exact form y 21 18...
- Q Verify the identity sin w sin w cos w tan w 1 tan w
- Q Verify the identity sin t cos t 2 sec t csc t sin t cos t sin t cos t sin t cos t sin t 2 sin t cos...
- Q Verify the identity csc x sec x cos x cot x tan x cos x sin x
- Q Sketch a graph of f z 0 5z 21 1 Before sketching the graph determine where the function has its minimum or maximum value so you can place your first...
- Q Make the indicated trigonometric substitution in the given algebraic expression and simplify see Example 7 Assume that 0 0 1 2 9 x x 3 sin 0
- Q 77 x Analyze the polynomial function f x The graph of f behaves like y 32 7x 7x 21 Answer parts a through h www for large values of x...
- Q Concavity and points of inflection Answer the following questions using the function f x e The first derivative of the given function is The second derivative of the given function...
- Q 1 3 3 Analyze the polynomial function f x 7x7x 7x 21 Answer parts a through h a Determine the end behavior of the graph of the function 1 3...
- Q Bonus 5 points Write a function such that f x f x 0 e
- Q 4 Find an antiderivative of the given function a f x x x b f x 3e2x x 1 x d f x 2 cos x e f x sin...
- Q 2 1 point Write 3 different equations f x g x and h x such that 2 f x g x h x x
- Q 5 3 points 1 5 points each Determine the derivative of each function a f t 24 e 7 b g x e 5 67
- Q 4 5 points Consider the following function f x 5x 7x 3 a 3 points Determine the equation of the tangent line to f x at x 1 b 1...
- Q Prove the identity tan x 1 3 x T 3 1 3 tan x 1 3 tan x tan x tan 3 3 tan x 1 3 tan x
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