Calculus Questions

2 A particle moves with position function s t4 4t 20t 20t t 0 a At what time does the particle have a velocity of 20 m b At what time is the acceleration 0 What is the significance of this value of t

The slope of the tangent line to the parabola y 2x 2x 5 at the point 3 29 is The equation of this tangent line can be written in the form y mx b where m is and where b is Question Help Video

5 4 3 2 1 V 4 3 2 1 23 3 4 L List all the numbers x at which the function graphed above is not differentiable Separate answers L commas

If f x 7 then f x T

50x7 25x6 20 5x Type your answer without negative exponents Simplify completely Find the derivative of

3 If f x 2 X Find f 3 3 x2 find f x

Find the derivative of 4x 8 2x 6

If f x 3x8 7x5 3x87x5 6x 5x find f x

Next question 10 1 If f x x 0 then f x Get a similar question 2 If g x 3x7 then g x 10 1 10x You can

OA The solution set is u 0 OB The solution set is OC The solution set is the set of real numbers OD The solution set is the empty set 10 5 0 y f x 7 0 10 What is the solution set of f x 0 Select the correct choice below and if necessary fill in the answer box to c your choice

olve the following inequality x 15x 54 0 The solution is Type your answer in interval notation Use integers or fractions for any numbers in the exp exact answer using radicals as needed

Sketch a graph of f x ax bx c that satisfies the set of conditions below a 0 b 4ac 0 Choose the correct answer below O A OB LEN OD

k k 5 5 The solution set is Use a comma to separate answers Type exact answers using radica

Solve for the specified variable n q y for n n HIE Type an exact answer using radicals as needed

r X 1 0 The solution set is 0 Type an exact answer using Express complex numbers in integers or fractions for any r expression Use a comma to as needed

Evaluate the discriminant and use it to determine the number of real solutions of the equation If the equati have real solutions tell whether they are rational or irrational Do not actually solve the equation 9x 18x 9 0 www Which of the following is the correct formula for the discriminant of the quadratic equation ax bx c 0 O b b 4ac O b 4ac O b b 4ac O b 4ac

Solve the following equation For an equation with real solutions support your answer graphically x 81 The solution set is Use a comma to separate answers Express complex numbers in terms of i

ve the following equation For an equation with a real solution support your answers gr 4 9x 2x 0 EER e solution set is ype an integer or a simplified fraction Use a comma to separate answers as needed

K equation FO an equation with real solutions support the answe x 8x 9 Rewrite the equation in factored form 0 0 Factor completely

3x 21 quation For an eq ition with real utions support your answer graphicall he solution set is Type an exact answer using radicals as needed Use a comma to separate answers as needed E umbers in terms of

rite the number without a negative radical 7 7 Simplify your answer

For the given complex number a state the real part b state the Imaginary part and pure imaginary or nonreal complex 2 9i a What is the real part of 2 9i 2 b What is the imaginary part of 2 9i 9 c Identify the number 2 9i Select all that apply A pure imaginary B nonreal complex C real y the nu

10 If a ball is thrown vertically upward with a velocity of 80 ft s then its height after t seconds is s 80t 16t2 a What is the maximum height reached by the ball b What is the velocity of the ball when it is 96 ft above the ground on its way up On its way down

5 Graphs of the velocity functions of two particles are shown where t is measured in seconds When is each particle speeding up When is it slowing down Explain a b VA VA 0 1 0 1

16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 5 FA 10 15 20 25 A quadratic model C t for the cost of tuition at a small private college in dollars for t years since 1990 is C t 8 28t 269 05t 3500 Find the equation of the tangent line for tuition in 2017 y mt b where m The tangent line estimate for tuition in 2017 is and b n M

DETAILS 07 A ladder that is 15 feet long leans against the side of a house The angle of elevation of the ladder is 80 Find the height from the top of the ladder one decimal place ft the ground Round your dis

Suppose f 5 9 and f 5 2 1 The equation of the tangent line of f at 5 is t x 2 Approximate f 5 46 to the nearest 2 decimal places f 5 46 A

Suppose is a continuous function where f 10 6 and f 10 3 The equation of the line tangent to the graph of y f x at x 10 will be y So f x Based on this f 10 8 A solution to f x 0 is a for a close to a 10

Suppose f is a function with 7 30 and f 7 3 Using the local linearization L x at x 7 estimate the following values of f f 10 L 10 f 6 f 6 5 Samotne

Let f x We wish to use linear approximation to approximate the values of f x when is close to 36 At x 36 what point is on the graph of f x Point At Jumanni Comm Slope 36 what is the slope of the tangent line to f x

5 4 3 2 5 Add Work 4 3 2 3 5 to In the above graph estimate the slope of the tangent line at x 4

An airplane flies at an altitude of 6 miles toward a point directly over an observer Consider 0 and x as shown in the figure To a Write 8 as a function of x 8 0 6 mi b Find 8 when x 14 miles and x 7 miles Round your answers to one decimal place x 14 miles 8 x 7 miles 0 O Not drawn to scale

Come up with an algebraic expression for a function with exactly two discontinuities It can contain familiar functions and it can be a piecewise function Your task will be to find the discontinuities in another team s function Answer

er leans against the side of a house How far is the bottom of the ladder from the side of the house when the angle of elevation answer to the nearest tenth 69 0 X

Find all k such that g x k Answer x 2x x 2 if x 2 if x 2 is continuous

Jenny and Jim are standing on a riverbank at points A and B respectively See the figure below Jim is 160 meters from a house located across the river at point C Suppose that angle A angle BAC is 41 and angle B angle ABC is 73 How far are Jenny and Jim standing from one another Round your answer to the nearest tenth of a meter 4 0 meters X

A pilot is flying over the ocean She determines that the angles of depression to two ships are 52 and 45 as shown in the figure below The plane is 2 miles from the ship located at point 4 How far apart are the ships Round your answer to the nearest tenth of a mile 2 mi B miles X

Evaluate the integral In 15x St 3 X In 15x 3 dx dx

avi and Carmen are standing on a riverbank at points A and B respectively See the figure below Carmen is 180 meters from a house located across the ver at point C Suppose that angle A angle BAC is 55 and angle B angle ABC is 73 How far are Ravi and Carmen standing from one another Round our answer to the nearest tenth of a meter 55 44 73 180 10 1 meters X

Find the following limit x 16 8 lim x 4 x 4

Use the sign chart for y f x below to determine where f x 0 f x I 4 Choose all that apply 0 3 00 3 0 0 1 1 0 4 4 1 0 1 1 1 3 0 4 1 O 1 3 Und 1 13 110 Und 3

ountain officials want to build a new ski lift from B to C as shown in the figure below The distance from A to C is 1530 feet They measure angle DAC to be and angle DBC to be 20 What is the distance from A to B Round your answer to the nearest tenth of a foot 1530 ft 40 A 20 feet

What is the first derivative of f z ln 42 3z 5

Consider a triangle ABC like the one below Suppose that B 58 C 67 and a 30 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or A 0 b 0 c 0 or O X No solution

Determine the derivative of f z 2e 1

Determine the derivative of f x 1 5

sketch the triangle O LA 50 25 73 c 270 O 2C 57 B B 270 73 73 270 50 50 C A O A A Solve the triangle using the Law of Sines Round side lengths to the nearest Integer a 208 962 x b 175 34 50 50 270 270 73 73 B B

Consider a triangle ABC like the one below Suppose that A 112 B 36 and c 60 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or C a b 0 or X No solution

Determine the derivative of the function f x 225 3e6e

f x x 3 2 x 3 x 3 x 3 1 Evaluate f 3 in the piecewise function above Type a response