Differentiation Questions and Answers

lim and the right hand limit lim 4x 1 According to the definition of the derivative to compute f 0 we need to compute the left hand limit We conclude that f 0 is undefined 3z 6z 42 2 for a 0 for a 0 which is undefined which is 0

10 u IgNslkr7j8P3jH 1BhBKplvJLUg6NO6tj9qFltz6nQLC 1 Homework C1S4 Question 5 of 7 1 point Question Attempt 2 0 5 m 3 Use slope intercept form to write an equation Write the equation using function notation whe 2 3 4

termine if the lines defined by the given equa 5y 10 3 x The lines are parallel O perpendicular O neither parallel nor perpendicular

0 0312 one of the answe questions remain

A system of linear equations in two variables has 2 solutions if it contains two non parallel lines that are not the same line O True O False

roblem Problem List Next Proble f x 68 x of the tangent line to the graph of f x a n of the tangent line to the graph of f pe at x 4 is given by 4 h f 4

nment 4 Prob oblem Problem List Nex definition of the derivative to ca

Given that f x h x cos x 3 2 h h Calculate f 3 T 2 37 2 5 6 3 T 2

If f x 3x sin x cos x find f x Find f 2

If f x f x 2x tan x Find f 5 sec x find

y 0 5 x 3 find equation of a line that goes through point 1 3 and is perpendicular to the above line Oy 2x 1 Oy 2x 5 Oy 2x 1

Suppose that f is a differentiable function such that f 1 5 and f 1 3 Use the product rule to compute h 1 if h x xf x cos x Enter your answer as a decimal Round to three decimal places as needed

A company buys a new bulldozer for 125550 The company depreciates the bulldozer linearly over its useful life of 23 years Its salvage value at the end of 23 years is 14000 Depreciation is the decrease or loss in value of the equipment due to age wear or market conditions

Graph the solution set of the inequality where

Solve for the unknown quantities in the triangle Round values to the nearest tenth a 27 b 34 c 44 OA C 81 6 A 37 4 B 61 0 OB No triangle exists C C 91 6 A 37 8 B50 6 D C 34 7 A 20 5 B 124 8

Find the value of the indicated trigonometric function of the angle 0 in the figure Rationalize the denominator where necessary Find cos 0 10 OA 10 51 51 OB 7 10 OC 7 51 51 OD 51 10

Find the trigonometric function value of the corresponding complimentary angle Given that sin 40 0 6428 find cos 50 OA 0 6428 OB 0 7660 O C 1 305 D 0 8391

Using the slope formula find th 7 2 and 4 2 What is the slope of the line Se choice

V D O Write a conditional statement that the Venn diag

Write a conditional statement that the Venn d

se logarithmic erivative x x x x 3 6 x 7 differentiation to determine the

Let x f f x 2ln sin x

Suppose that f x ln 5x 10 Find f x and use interval notation to give the domain of f Note When entering interval notation in WeBWork use I for I for and U for the union symbol If the set is empty enter without the quotation marks f x

40 tan 120 OA 3 O O O O OB co cor D 3 OC 3 3

7x 8 0 equal 9 Determine the value of k which will make the roots of the equation 16x 8x 3 k are equal

7 Express 3500 in scientific notation that indicates it has two significant digits You may need to round A 3 5 10 OB 3 5 x 104 3 5 x 10 C D 3 5 x 105

d the interest on the following loan Assume 365 days in a year 34 200 at 10 25 for 101 days C e simple interest on 34 200 at 10 25 for 101 days is ound to the nearest cent as needed

Which function below is an ODD function f x x x f x 4x 2x f x 2x 8x f x 3x 5x

E Fill in the blanks To graph y x 4 you shift the g

Use the given graph of f to find a number such that if 0 x 31 5 then If x 21 0 y 9 R 2 5 2 1 5 26 3 3 8

d y dx f x f x x 1 b x b 0 otherwise

Assume that the functions f and g are differentiable Find the derivative using the table belc x 1 f x 4 g x 4 f x 2 1 g x 1 3 a If K x K 1 b If H x H 1 2 3 c If W x g x f x 3 2 3 1 f x g x 1 2 1 3 3 2 find find f x 3x 1 4 find

Let f x 4 x f x 6 x x

Given the following functions f x cos x g x x 7 1 Find f g x and g f x Use symbolic notation and fractions where needed d dx f g x dg f x

Calculate the following derivatives Use symbolic notation and fractions where needed d dx cos 2x x d cos x 8 dx d dx cos tan 5x

Use the table of values to calculate the derivative of the function at the given point 1 4 6 4 0 10 5 78 4 1 6 17 Give your answer as a whole number S x f x f x g x g x 5 de f g x dx 1x 6

Use the General Power Rule Exponential Rule or the Chain Rule to compute the derivative y e 7x 19 Use symbolic notation and fractions where needed de17x 19 1

Use the Chain Rule to find the derivative y cos e46 Express numbers in exact form Use symbolic notation and fractions where needed dy

Compute the derivative of the function y using derivative rules y 9 3x sin x Express numbers in exact form Use symbolic notation and fractions where needed dy dx

The height at time t in seconds of a mass oscillating at the end of a spring is s t 300 32 sin t cm Find the velocity and acceleration at t Use symbolic notation and fractions where needed v t cm

Find the derivative of f x 6 sec x 11 cot x Use symbolic notation and fractions where needed f x

Find the derivative of f x 15x tan x Use symbolic notation and fractions where needed

1 point Given that f 8 5 2 and f 8 4 5 8 approximate f 8 5 f 8 5

5 Find the are length of the curve r t 3ti 2 t2 k over the interval 0 t 3

Given that f 5 10 and f 5 2 approximate f 5 4 f 5 4

Given f x 7 x 2 find f x using the limit definition of the derivative 1 7 x 2 f x X

Below is the plot of a function f x D 8 X 6 3 nc 0 1 5 6 53 3 Xx Which is the most accurate table for the derivative function f x f x f x f x 0 0 0 1 4 2 7 1 7 0 0 5 4 4 2 1 7 4 1 6 3 050 1 5 15 14 43 42 10 9 8 3 6 5 2 6 x7 8 9 10 H 14 15 0 x 6 3 lo 0 1 5 3 1 4 4 1 I 6 3 0 1 5 52 3 f x 0 7 0 8 5 84 4 1

Find the derivative of the following function 3 f w W 2 4 f w

Calculate the unit step response of the system whose governing equation is t de The coefficient of the est term in the output function is 0 2 0 25 0 04 0 2 u

ons from a Graph The graph of one period of a function of the form y a sin k x b or y a cos k x b is shown Determine the function 37 YA 5 39 1 0 5 3 1 0 y 1 2 CO CEN TT 4 11 213 3 X 20 2 3 2 x 38 YA 40 0 1 2 AX YA A 2 4 X BOS