Differentiation Questions and Answers

Note Triangle may not be drawn to scale Suppose a 10 and b 2 sin A Find an exact value cos A tan A b sec A A CSC A cot A

If there are n of type 1 n of type 2 and so on using the following formula

3 Four amateur miniature golfers attempt to finish Each round of 100 the number of holes they suc recorded Due to the presence of extreme values the best representation for the data List the four from least to greatest player a player

olve the following system of equations using matrices row operations If the system has no solution say that it is inconsister 2x 3y 2 6x 3y 10 elect the correct choice below and if necessary fill in the answer box es to complete your choice A The solution is Simplify your answers B There are infinitely many solutions The solution can be written as x y x Simplify your answer Type an expression using y as the variable The system is inconsistent y is any real number

Question 6 12 2 23 Part 2 of 2 rite the system of equations corresponding to the augmented matrix Then perform the r ugmented matrix hich of the following is the system of equations corresponding to the augmented matrix

Question 5 Part 2 o system of equations corresponding to the given augmented matrix us 9 13

Use the Laws of Logarithms to combine the expression log2 x29 log x 3

Use the Laws of Logarithms to expand the expression In

5 4 3 SH s 4 3 cha 2 7 My 2 3 4 5 List all the numbers x at which the function graphed above is not differentiable Separate ans using commas

if x 6 6 Find the value of b so that f x is continuous Suppose f x b 4x 4 8x b if

Determine the domain and range of the function Part 1 of 2 BENET The domain of the function in interval notation is Part 2 of 2 The range of the function in interval notation is 10 0 0 0 0 D X IC 00

A committee of 5 st a In how many way b In how many way

10 For the function determine the following values Restriction Hole s V A H A x intercept y intercept f x 2x 7x 6 x x 2 f x x 2x 3 x 1 f x 3x 6 2x 4 g x x 2 X 4 g x 2x x 1 g x x 2 x2 5x 4 H

Graph the feasible region for the given system x 3y 12 3x y 12 x 0

If f x In x a fog x What is the domain of fog b gof x What is the domain of g of c fog 7 d fo h x What is the domain offo h e foh e g x e7x and h x x find the following

Find the following derivatives z and Z where z 6xy x y x 5s 5t and y 5s 5t dz ds Type an expression using s and t as the variables 11 5 6x x dy Type an expression using x and y as the variables x dy s Type an expression using s and t as the variables dy 5 5 dt Type an expression using s and t as the variables 5 at Type an expression using s and t as the variables 375s 250st 125t 300s Type an expression using s and t as the variables 4 Type an expression using s and t as the variables

47 Describe the graph of the equation r cos 8 2 A a line perpendicular to the polar axis passing through the point 2 0 B a line parallel to the polar axis and a distance of 2 below it C a line perpendicular to the polar axis passing through the point 2 90 D a line parallel to the polar axis and a distance of 2 above it

36 Find the square roots of 36 cos 152 i sin 152 Leave your results in polar form What is one of the answers A 6 cos 301 i sin 301 OB 6 cos 211 i sin 211 C 6 cos 346 i sin 346 D 6 cos 256 i sin 256

33 1 i in trigonometric form OA OOO B C D 2 cos 225 i sin 225 2 cos 135 i sin 135 2 cos 225 i sin 225 2 cos 135 i sin 135

Question 4 3 5 4 3 2 1 2 3 1 2 3 4 5 a At the point shown on the function above which of the following is true Of 0 f 0 Of 0 f 0 f 0 f 0 f 0 f 0

5 4 3 2 4 3 2 7 2 3 4 2 4 tert 5 q At the point shown on the function above which of the following is tru Of 0 and f 0 Of 0 and f 0 Of 0 and f 0 Of 0 and f 0

The graph of y f x has f 5 might be a graph of y f x Look carefully at all eight choices H a 2 f 5 2 and f 5 of a 2 Which of the following

Differentiate the given function f t 6ln t 7t O 7t 6 2t f t 1 f t 2 6ln t 7t f t 6ln t 7t 7t 6 2 6ln t 7t 7t 6 f t 2t 6ln t 7t

Differentiate the given function f x xe x3 O O O O f x e x3 f x 3e X 1 e x f x 3x e x f x e x3 xe xe x2

Differentiate the given function f x e 5x x4 O f x 5e 6x 4x O f x 5e 5x 3x f x 5e 5x 4x f x e 5x 4x

Differentiate f x ln 9x 8x 5 O 27x 8 f x 9x 8x 5 O O O the given function 1 f x 9 3 8x 5 27x 8 f x 9x 8x 5 f x 27x 8 9x 8x 5

3 3i 5 4 3 2 1 4 3 2 1 1 2 3 4 5 1 2 3 4 5

Add 4 7i 14 sum Subtract 4 7i 1 difference Calculator

Question I et f x 6x 53x 1 ccording to the rational root rational roots of this polyno 5 1 1 1 7

The function T C describes the number of turtles in a pet store in Phoenix Arizona when there are C cats in the store Interpret the meaning of the following T 8 17 We will assume that any change in the cats and turtles population is a result of them being sold to a loving farnily 17 turtles are being sold per cat sold when there are 8 cats in the store 8 cats are being sold per turtle sold when there are 17 turtles in the store 17 turtles are being sold per 8 cats sold There are 17 cats in the pet store when there are 8 turtles 8 cats are being sold per 17 turtles sold There are 8 cats in the pet store when there are 17 turtles

The function P D describes the number of people in Arizona D days after the new year Interpre the meaning of the following P 2 80000 in the answer box below Approximately 80000 people are leaving Arizona every two days About 80000 people are leaving Arizona per day on January 2nd There are about 80000 people in Arizona on January 2nd The change in people is about 80000 on January 2nd There are negative 80000 people in Arizona on January 2nd There are two people leaving Arizona on the 80000 day of the year

8 7 6 5 the TI 2 My 1 2 071 pt C Based on the graph above estimate to one decimal place the average rate of change from x 4

Find a point on the surface z tan y In x where the tangent plane is parallel to the plane x 2y2z 0 Hint the surface 2 tan y In x is the graph of the function f x y tan y In x

Write an equation for the function grap 7 6 5 4 3 2 1 1 77 H N

3 200163 2 ft P Tist lift z ft 1 75 25 Consider the frame Find the reactions in E Find the x andy internal forces in the frame ie the joints Find the Sheanand tension at J Find the bending Movent at J Do not forget to use free body diagrams

Let f x 1 42 6 f x h f x h Expand and simplify Enter the expression in reduced for

This is the graph of a function among the following functions 5 5 5 16 55 p 5 154 15 5 1st Choose the graph of its derivative from 5 5 q

Suppose that f is a function given as f x 3x 4x 2 Simplify the expression f x h f x h Simplify the difference quotient f x h f x h f x h f x h The derivative of the function at is the limit of the difference quotient as h approaches ze f x lim f x h f x h 0 h

Given f f x 7 73 find f x using the limit definition of the derivative

If f x 6x 11 use the limit definition of the derivative to evaluate f x

From a pack of 52 cards two cards are drawn together at random What is the probability 1 mark of both the cards being kings

A bag contains 2 red 3 green and 2 blue balls Two balls are drawn at random one after the other What is the probability that none of the balls drawn is blue 1 mark

7 Consider the function g x x which is defined for all 0 Observe that imzo g z is indeterminate due to its form of 0 Think about how we know that 0 0 for all k 0 while b 1 for all b 0 but that neither rule can apply to 0 a Let h x ln g x Explain why h x 2x ln x b Next explain why it is equivalent to write h x c Use L H pital s Rule and your work in b to compute limo h x d Based on the value of limo h x determine limo g x

1 L H pital s Rule with graphs For the figures below determine the nature of lim za the blue curve and g x as the black curve lim HI a g g x o positive o negative O zero o undefined Activate lim P g x f x g x positive o negative zero o undefined if f x is shown

Find by implicit differentiation dy dx dy dx 47 y 4 X 11 11 x3 13 9 X

Find the first and secon f x LO 5 X 6x

Question 2 let f x x 3 x x 12 Find equations of ALL vert

Verify the following equation without using your calculator Show all your work 12 14 Cos 1 5 13 2 Sin 1 Cos 56 65

Solve the following logarithmic equations 16 2log3 x 4 log39 2

If sin 0 cos 0 7 and is in the 3rd quadrant find the exact value for cos 0 9