Application of derivatives Questions and Answers

5 4 3 2 3 4 2 56 2 3 2 w 5 q In the above graph of y f x find the slope of the secant line through the points 2 f 2 and

5 4 3 2 7 1 3 2 t 2 3 4 m f 5 q In the above graph of y f x find the slope of the secant line through the points 4 f 4 and 3

The half life of Sodium 24 is 14 96 hours If a sample contains 170 mg how many mg will remain after 170 hours ma

Let h x x 6x 8 The absolute minimum value of h over the closed interval 1 x 6 occurs at what z value Choose 1 answer A 0 B 4 1

Write In a b 4 ln a b 5 ln c numbers In single logarithm Assume all arguments represent positive syntax error

Evaluate the radical expression and express the result in the form a bi Simplify your answer completely 8 7 1 1 8 5 8 5

x x 2 x 1 a Find the following limits If an answer does not exist enter DNE Let g x i ii lim g x 1 1 lim g x X 1 X

Evaluate the power and write the result in the form a bi Simplify your answer completely 51 4

In traveling across flat land you notice a mountain directly in front of you Its angle of elevation to the peak is 3 5 After yo drive x 13 miles closer to the mountain the angle of elevation is 9 Approximate the height of the mountain Round your answer to one decimal place mi 3 50

1 point Find the surface area of the region S on the plane z 2x 5y such that 0 x 30 and 0 y 5 by finding a parameterization of the surface and then calculating the surface area A parameterization is x s t y s t z s t S t Then the surface area and and with

12 51 A car starts from rest and travels along a straight road with a velocity described by the graph Determine the total distance traveled until the car stops Construct the s t and a t graphs v m s 30 I 30 60 v 0 5t 45 90 s

Find the domain of the function f x 4 X 9 The domain is 0

Calculate f x y z dS For Is f x y z ds y 3 z 0 x z 9 f x y z z

Compute the surface integral over the given oriented surface F y i 2j xk JF ds portion of the plane x y z 1 in the octant x y z 0 downward pointing normal

Calculate f x y z dS For Is f x y z dS x y 25 0 z 7 f x y z ez

1 point For the surface with parametric equations r s t st s t s t find the equation of the tangent plane at 2 3 1 Find the surface area under the restriction f 1

1 point Consider the cone shown below If the height of the cone is 6 and the base radius is 3 write a parameterization of the cone in terms of r s and 0 t x s t y s t z s t s t and 1 and with

1 point Parameterize the plane through the point 1 5 1 with the normal vector 5 4 4 7 s t Uses and t for the parameters in your parameterization and enter your vector as a single vector with angle brackets e g as 1 s t s t

1 point Find parametric equations for the sphere centered at the origin and with radius 5 Use the parameters s and t in your answer x s t y s t z s t s and 3 and where

1 point Compute the curl of the vector field F 2y 7 sin x cos z k curl

7 Consider the addition of 15 4 to 28 What would a mathematician say the answer is What would a scientist say Justify the scientist s answer not merely citing the rule but explaining it

Evaluate I sin x 9y dx 5x y dy for the nonclosed path ABCD in the figure I D C B A 0 0 B 4 4 C 4 8 D 0 12

ne integral x z ds where C is the line segment from 0 1 2 to 6 3 4

1 point Let F x y 2Q A Compute dx B Compute Note Your answer should be an expression of x and y e g 3xy y ap dy yi xj x x and let C be the circle r t cost i sin t j 0 1 2 C ComputeF dr Note Your answer should be an expression of x and y e g 3xy y Note Your answer should be a number he wholo xy plane 2

Compute the line integral of the scalar function f x y z 2x 8z over the curve c t e t t 0 t 9 Sc f x y z ds

egral 3xy2 ds where C is the right half of the circle x y 25 3xy

Use cylindrical coordinates to calculate f x y z dV for the given function and region f x y z z x y z 36 Jw f x y z dV

Consider the function defined by f x x bx cx d a Find f x using first principles b The graph off has a local maximum and a local minimum point Show that b2 3c

Given f x f x 4x 13 9x 7 findf x

Find the slope and y intercept of the line If an answer does not exist enter DNE 7x 8y 16 slope y intercept x y Draw its graph S No Solution 10 9 8 7 6 7 8 0 2 5 4 3 10 10 9 8 7 6 5 4 3 N W 2 4 1 4 t N 4 2 3 4 5 6 7 8 2 7 8 9 10 Clear All Delete Fill Graph Lay Line 1 Point 1 Point 2

r Acevedo was told to drink at least 3 L per day You should tell him this is malysis and round your answer to nearest tenth Use either proportion or dimensional

6 4 6 5 i If f Q Q is given by f x b f 5 a f 9 c f 0 i If the function f 5 2 11 4 be defined by f x x 5x 9 find f 8 and f 9 ii If the function f R 1 be defined by f x x 1 find f 5 F 8 Objective

6 14 If f x A 1 x 1 x 1 y 1 y y then f y B 1 y 1 y C y 1 y 1 D y 1 y 1

Dally oil production from Mexico 5 national oil company can be approximated by q t 0 015 t 2 0 1 t 5 11 quad text million barrels 8 leq t leq 13 where t is time in years since the start of 2000 At the start of 2010 the price of oil was 86 per barrel and decreasing at a rate of 19 per year How fast was the company s daily oil revenue changing at that time The daily revenue was at a rate of dollars per year Remember that q t is measured in millions of barrels so you will need to account for this in your revenue calculations

Which of the lines in the following graph appear to be tangent lines Why or why not W Which of the lines in the following graph appear to be tangent lines Select all that apply DA 3 DC 4 DE 42 CIXED B LA D Lg OF 4 Why do the lines selected above appear to be tangent lines and why are the other line s not tangent lines OA The slope of each tangent line is approximately zero The slope s of the other line s are undefined OB Each tangent line is perpendicular to the graph at the point of intersection between the graph and the respective tangent line The other line s are not perpendicular to the graph at the point of tang OC The slope of each tangent line is equal to the slope of the graph at the point of intersection between the graph and the respective tangent line The other line s are not parallel to the graph at the p OB The slope of each selected tangent line appears to be undefined The other line s are parallel to the graph at the point of tangency

Assume that f is continuous on a b and f x dx 0 Does it necessarily follow that a f x 0 for at least some x a b b Sof x dx 0 c all upper sums U P are positive d f f x 2 dx 0

Classify the statement as either true or false If f is continuous at x 3 then f 3 does not exist Choose the correct answer below O true O false

Give exact answers no decimals If more than one answer separate them with a comma Enter pi for Consider the function y 3 sin x Where are the zeros of this function on the interval 0 2 What is the maximum value of this function on the interval 0 2 At what values of a in the interval 0 2 does this largest value occur Note You can earn partial credit on this problem

Find the volume of the solid generated when R shaded region is revolved about the given line I x 2 sec y x 2 y 3 and y 0 about x 2 The volume of the solid obtained by revolving the region about x 2 is X 3

1 point Use cylindrical coordinates to evaluate the triple integral z 1 9 x y and the xy plane dV where E is the solid bounded by the circular paraboloid

Simplify the expression 624 5x6 5x using factoring and exponential rul

What are the rectangular coordinates of the point whose cylindrical coordinates are r 4 0 2 z 5 X y 7

Do zety dV where B is the box determined by Evaluate 0 x 5 0 y 5 and 0 z 2 The value is

Determine the intervals where the value of f x is positive when f x x 7 2x 3 x 5 Choose all that apply

A rectangle has a perimeter of 6x 3 9x 2 10x 5 and a length of x Find the width of the rectangle when the length is 21 inches

Find a polar equation for the conic A focus is at the pole e 3 5 directrix is perpendicular to the polar 4 iaxis to the left of the pole

A student is speeding down Route 11 in his fancy red Porsche when his radar system warns him of an obstacle 400 feet ahead He immediately applies the brakes starts to slow down and spots a skunk in the road directly ahead of him The black box in the Porsche records the car s speed every two seconds producing the following table The speed decreases throughout the 10 seconds it takes to stop although not necessarily at a uniform rate Time since brakes applied sec 0 2 4 6 8 10 Speed ft sec 120 85 50 20 15 0 A Use a left hand sum and right hand sum to estimate the total distance the student s car traveled before coming to rest left hand sum right hand sum include units B Which one of the following statements can you justify from the information given A The car stopped before getting to the skunk B The skunk was hit by the car C The black box data is inconclusive The skunk may or may not have been hit

A car comes to a stop six seconds after the driver applies the brakes While the brakes are on the following velocities are recorded Time since brakes applied sec 0 2 4 6 Velocity ft s 8945 160 Give lower and upper estimates using all of the available data for the distance the car traveled after the brakes were applied lower upper for each include units On a sketch of velocity against time show the lower and upper estimates you found above

1 point For the region R below write Rf dA as an iterated integral in polar coordinates 1 b JRfdA ffd where dA With a Note Usef for 0 in your expressions C 5 and d d d

A lamina occupies the region inside the circle x y2 12y but outside the circle x y2 36 The density at each point is inversely proportional t its distance from the orgin Where is the center of mass