Limits & Continuity Questions and Answers

Find the roots of the equation z 27i 0 in the form a bi

2 1 The slope of the tangent line to the curve y at the point 8 X is The equation of this tangent line can be written in the form y mx b where m is b is

Consider the following 0 cos 3 Find the length of the third side of the triangle in terms of x e tan X Find in terms of x for all three inverse trigonometric functions e sin

Equation Given two points x y and x2 y2 the equation for the line that passes through these two 1 1 x X X 0 y V V2 Use this determinant to find the equation for the line that passes through the points 2 7 and 4 4 Write the final answer in slope intercept form 8 pts points is given by a

Find the difference quotient Find f 0 Find f x by determining lim h 0 Find f 2 This slope should match the tangent line you drew above Clear Al DEBULL Find f 1 Graph the function f x 2x and draw the tangent lines to the graph at points whose x coordinates are 2 0 and 1 10 9 8 7 f x h f x h 6 5 3 f x h f x h 4x 2h

11 4 2 0 0 1 the matrix product AB defined Let A 0 2 B 1 1 1 3 3 3 D B 3 2 5 3 2 2 DB 1 2 3 B 2 For which of the following matrices is

6 8 1 4 0 2 1 1 3 following matrices is equal to the linear combination A 3B Let A 9 1 329 O 123 7 9 O 8 4 13 3 0 1 4 and B Which of the

Complete the following questions a b 24 is 5 of 5 of what amount is 6 00 Answer

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an A parking garage cha maximum length of tim

5 16253649648 The next seven dig

Use the graph of f in the figure to do the following a Find the values of x in the interval 0 5 at which f is not continuous b Find the values of x in the interval 0 5 at which f is not differentiable Ay 20 16 12 8 4 0 4 8 12 16 20 Q a In the interval 0 5 f is not continuous at x Use a comma to separate answers as needed b In the interval 0 5 f is not differentiable at x Use a comma to separate answers as needed

ometimes even when we are not sure whether or not a particular limit exists we can still use algebra t now that there are only a small number of possible values the limit could take a Last week in tutorial we saw that lim tan sin It also happens to be true though we will no x 0 x3 3 verify it at this time that lim tan x 2 Suppose that lim sin exists Determine the value sin the limit Hint This is a special case of part b x 0 b Suppose f x g x and h x are three functions with lim f x xc g x f x i If M 1 show that either lim ii What can you say if M 1 M and lim f x g x h x X C ML 1 M or the limit does not exist L

Write the standard form of the equation and the gene Then graph the circle r 5 hk 3 4

22 tan 52 tan 57 12 1 tan 51A 2 tan 7 1 7 and cost 1 13 45 055 sandt in quadrant

In Sarah s community the Primary school bell rings every 30 minutes and the High school rings every 40 minutes Both schools start at 8 00am Determine at what time the bells ring at the same time between 8 30 am and 11 am Show all possible calculations 5

K What is the shading style of the for The forty first figure in the sequenc

Which option describes the end behavior of the function f x 5 x 6 x 3 3x 2

K Ty CM 3 32 Part 1 of 5 Fill in the reason that justifies each step ZCDE and ZEDF are supplementary mZCDE mZEDF 180 x 4x 20 180 5x20 180 5x 200 x 40 4 that form supplemen a b c d e

Find the interval of convergence for x 2 n 2 n 1

Find each of the following functions f x 5 x g x x 4 a f g State the domain of the function Enter your answer using interval notation b f g State the domain of the function Enter your answer using interval notation c fg State the domain of the function Enter your answer using interval notation d f g State the domain of the function Enter your answer using interval notation

7 In the diagram segment JK Gl Solve for x if HJ 3x HK 2x KI 6x and JG 18 units a x 1 b x 2 a C d C X 4 d x 5 Ge H J K

Solve the eq 5x 4y The solution

Solve the compound set of the compound 5x 30 inequality solution ine 3x 6 and

Find the frost 5 terms a n 1 n 1 b d An n 1 1 n 1 3n an n 3 n 3 cos TT 6 n 0

The following are the cash flows of two projects Year Project A 0 81234 1 2 3 4 330 160 160 160 160 Project B 330 230 Project A B If the opportunity cost of capital is 12 what is the profitability index for each project Note Do not round intermediate calculations Round your answers to 4 decimal place 230 230 Profitability Index

Use the formula to f A bh find A when answer is A

and Solve the equation 3 9x 3 2 8 5 Que

and Operations Equations K Solve the equation 1 X 3 9 9 3

14 10 points Let 0 0 0 5 0 2 3 and B I A IA Find I B A 10 2 3 0 4 0 1 I 1000 0 1 0 0 0010 0 0 0 1

Domain Range 6 Domain Range X O 49 Function y 2345 YTON of Domain Range Function 8

Solve the equation 4 4n 3 2 3n 8

Explain your answers in words 1 You are given a graph how do you use VLT Vertical Line Test to decide if the given graph represents a function 2 When a function f x is given how do you evaluate f a b

can someone explain me how to do this problem also why do we multiply the First equation by 2 and not the second equation bh anything 36 Find the values of a and b that make f continuous everywhere x x 2 f x 1 4 ax 2x a b VT if x 2 bx 3 if 2 x 3 if x 3 45 2013

Fill in each matrix for diagonalization of the matrix A A PDP 1 5 Ex 5 2 1 1 6 10 2 3 1

valuate the function at the given numbers correct to six decimal places X 8 1 8 05 8 01 8 005 8 001 x 7x8 x 8x X 7 9 7 95 7 99 7 995 7 999 x 7x 8 x 8x uess the value of the limit if it exists Round your answer to three decimal places If an answer does not exist x 7x8

Graph the function and its inverse Include the domain restrictions 17 f x x 2 D D

Evaluate the limit et 1 7 lim t 0

nd the limit Use l Hospital s Rule if appropriate If there is a more elementary method consider using it 9x 9 XX 1 In x X 1

Ise l Hospital s Rule to find the exact value of the lim lim 5 4 X 0 3x 2

nd the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it lim sin 5x csc 7x X 0

lim f x 0 lim g x 0 x a b c lim p x x a d valuate the limits below where possible If a limit is indeterminate enter INDETERMINATE a lim f x x a g x lim f x x a p x h x lim x a p x lim h x X a p x lim x a q x lim g x 0 x a 1

5 Let f t te 2t and F x f f t dt a Determine F x b Use the First FTC to find a formula for F that does not involve an integra c Is F an increasing or decreasing function for a 0 Why

What is the value of loge 36 O 6 0 2 2 O6

Which of the following is a logarithmic function Oy log x Oy 3 Oy x 3 0 y x

8 Concentrated hydrochloric acid has a density of 1 19 g mL What is the mass of 250 0 mL of HCl aq

4 taxi service charges passengers a 2 flat fee plus 0 75 per mile Which equation shows the relationship between 7 the number of miles that a passenger ravels and t the total cost of the ride

G t Complete parts a and b below a Make tables of values of G at values of 1 cos 4t 4 3 t 1 t that approach bo 1 from above and below Then estimate lim G t t 1 yo not round until the final answer Then

The graph of y f a fox 3 x 4 is shown 4 3 2 1 54 125 Fo Ne esa 55 m 4 12 O a Select each value of a for which lim f x does not exist I a 2 0 1 2 b Select each value of a for which f is not continuous at a 2 0 1 2 3 O c Select each value of a for which f is not differentiable at a 2 0 1 2 3

a lim f x I 9 b lim f x I 9 c lim f x 1 9 f x x 12x 27 x315x2 27 243 help numbers