# Limits & Continuity Questions and Answers

Calculus
Limits & Continuity
The graph of y f x solid and y g x dashed is shown 6 5 4 3 4 lim 2 1 9 x 0 8 f x lim 24 1 g z Does Not Exist 88 0 8 2 z 1 g z Does Not Exist 0 Find the following limits 1 Does Not Exist 6 5 4 3 2 1 2 3 nd 5 6 2 3 4 1 1 1 1 S 6 q
Calculus
Limits & Continuity
6 Here is a graph of a pattern of numbers where V is a function of n The first point is 0 1 22 20 18 16 14 12 10 8 6 28 26 24 4 2 32 30 V 2 3 4 IMMathematics 5 a Plot the next 2 points on the graph that follow the pattern b Write an equation to describe the relationship between V and n f 1 1 f n f n 1 3 n 41 3 8
Calculus
Limits & Continuity
The graph below is the function f x 8 7 6 5 4 3 2 8 7 6 S 4 lim 118 32 4 12 2 3 3 4 5 6 7 4 6 8 1 2 3 4 5 6 7 8 96 f x ter the limit If the limit is m enter go If the limit is enter oo If no limit exists
Calculus
Limits & Continuity
A cyclist rides down a long straight road at a velocity in m min given by v t 100 10t for 0 st 10 a How far does the cyclist travel in the first 4 min b How far does the cyclist travel in the first 8 min c How far has the cyclist traveled when his velocity is 75 m min
Calculus
Limits & Continuity
Check all that apply sin 5x sin CT 5 5x 5x sin 6x 5x 6x sin 5x sin 6x 6 sin 5x 6x
Calculus
Limits & Continuity
The graph of y f x solid and y g x dashed is shown AT 4 3 Find the following limits f x lim 2 4 g x 0 lim f x lim 2 4 g z 8 Does Not Exist 0 2 1 f x g z Does Not Exist 6 5 4 3 2 1 1 2 3 A 5 6 1 2 3 4 5 6
Calculus
Limits & Continuity
State whether the function is continuous at the given x values Justify your answers sqvt done lar 2x 1 x 1 7 f x 2 2 1 x 4 x 4 a x 3x at x 1 b at x 4 2 4 1 4 3 4 3 4
Calculus
Limits & Continuity
The graph of y f x solid and y g x dashed is shown 6 5 4 B Find the following limits f x lim 1 g x 818 0 Does Not Exist f x lim 2 1 g x 00 Does Not Exist 1 f z lim 2 1 g x 6 5 4 3 2 1 2 3 4 5 6 3 4 5 6
Calculus
Limits & Continuity
Find the limit sin 7x lim x0 sin 6x lim x 0 tan 6x sin 7x
Calculus
Limits & Continuity
To find lim 2 0 cos x 1 which of the following steps might be useful 8 Multiplying numerator and denominator by Adding 1 to numerator and denominator Multiplying numerator and denominator by cos x 1
Calculus
Limits & Continuity
Evaluate 3 2 3x lim 4x sin 2 0
Calculus
Limits & Continuity
The graphs of y f x solid and y g x dashed are shown The two curves intersect at 5 0 Determine the sign of the following limits You may assume the limits exist lim f x g x is 5 Positive Negative Zero lim f x g x is 20 Positive Negative Zoro
Calculus
Limits & Continuity
Find the value s of k such that f x is continuous everywhere Sx 76 a 2 4x3 3kx 2 x 2 q f x
Calculus
Limits & Continuity
x 3x 7 x 3 3 x 1 x 1 8 g x 2x 1 In x a at x 3 ran b at x
Calculus
Limits & Continuity
Find the limit sin 5x 3x lim x 0 3x 40 sin 5x lim
Calculus
Limits & Continuity
The graph below is the function f x 8 7 6 5 4 3 2 lim f x 2 8 8 7 6 5 4 3 27 1 2 AWN 3 4 567 7 8 4 5 6 7 Enter the limit If the limit is o enter oo If the limit is enter oo If no limit exists enter
Calculus
Limits & Continuity
Suppose f x has the following values I f x lim 8 7 9 7 99 6 5 6 05 1 6 f T 7 999 8 6 005 9 appears to be 8 001 6 004 8 01 6 04 8 6
Calculus
Limits & Continuity
Given lim f x 2 and lim g x 1 evaluate 8118 8178 lim g x ln 6f x 4 8118 lim 8118 lim 8118 lim 8118 69 x e f z 6 2 49 x cos f x a x C
Calculus
Limits & Continuity
Evaluate the limit 4 6x lim I 11 4x Use oo if the limit is and oo if the limit is
Calculus
Limits & Continuity
Suppose lim f x 8 Find the following Type DNE if the limit does not exist 48 2 lim 8 f x 8 2 lim 2 8 f x 8 2 lim z 8 f x 8
Calculus
Limits & Continuity
Suppose lim f x 7 lim g x 3 x x x f x 5x 3 3x 1 lim 4 xxxg x
Calculus
Limits & Continuity
3 If fcx 3x x and g x 3x 2 find and simplify each of time fonowing a g x 5 b fC3D S c gcf 2 D e
Calculus
Limits & Continuity
What radical function is represented in the graph f x Simplify your answer 9 3 0 4 4 1 5 X
Calculus
Limits & Continuity
Find the value s of k such that f x is continuous everywhere x 7 4x3 3kx 2 O f x x 2 x 2
Calculus
Limits & Continuity
13 Let f be the function defined by f x value of a is f continuous at x 10 x 14x 40 x 10 a x 10 For what x 10
Calculus
Limits & Continuity
Sketch the lines through the point with the indicated slopes on the same set of coordinate axes Point 3 5 S No Solution a 5 10 9 8 7 6 b 3 fa Slopes c d Undefined 10 2 2 3 4 5 6 7 00 40 W 5 89 10 Graph Layers Line 1 Point 1
Calculus
Limits & Continuity
Suppose f x has the following values X 5 9 f x 5 5 1 2 6 5 f x lim 100 81 000 3 810 Undefined 1 lim z 6 5 f x 1 3 8 0 8 1 lim z 6 5 f x appears to be Undefined 1 3 5 99 5 05 appears to be 5 999 5 005 appears to be 6 8 6 001 4 999 6 01 4 99 6 1 4 9
Calculus
Limits & Continuity
Evaluate the limit 5x 10x 7x lim 818 4 3x 6x Use oo if the limit is oo and oo if the limit is o
Calculus
Limits & Continuity
24 Given lim f x 6 and lim g x 6 evaluate x 1 x 1 lim 6f x 4g x x 1 lim 6 4f x x 1 lim x 1 Ag 2 6f x 4g x 6 4f x lim 6f x 4g x 6 4 x x 1
Calculus
Limits & Continuity
The path r t t i 21 1 j describes motion on the parabola y 2x 1 Find the particle s velocity and acceleration vectors at t 3 and sketch them as vectors on the curve The velocity vector at t 3 is v 3 1 12 J Simplify your answer including any radicals Use integers or fractions for any numbers in the expression The acceleration vector at t 3 is a 3 0 i 4 j Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Choose the correct sketch for the particle s velocity and acceleration at t 3 O A OB 2 Q O C
Calculus
Limits & Continuity
Suppose lim f x 17 and f x is nonconstant x 5 Provided the limit exists 7 12 1 f x 10 lim x 5 f x 17 Question Help Video A Written Example
Calculus
Limits & Continuity
Given lim f x 8 and lim g x 7 evaluate x 3 I 3 lim 6 f x 3g x x 3 lim 6 3f x I 3 lim 2 3 off 6f x 3g x 6 3f x 2 lim 6f x 3g x 6 3f x z 3
Calculus
Limits & Continuity
8 x x if x 4 if x 4 2x 3 Calculate the following limits Enter DNE if the limit does not exist lim f x Let f x lim f x 2 4 lim f x 2 4 Question Help Video B Written Example
Calculus
Limits & Continuity
Find the domain of the function Enter your answer using interval notation g x 4 7x 0
Calculus
Limits & Continuity
Suppose f x 7x 5 6 Evaluate lim f x x 5
Calculus
Limits & Continuity
Find the limit x 8x 15 lim 3 3x 91 10 Written Example
Calculus
Limits & Continuity
Evaluate the limit 4x 16 4 x 12x 32 lim Video 2 Writ
Calculus
Limits & Continuity
Suppose you know that lim f x 16 x 9 Find the following 16 f x lim x 9 f x 4 FA
Calculus
Limits & Continuity
Evaluate the limit lim y 0 1 8 y Y 1 64 11
Calculus
Limits & Continuity
Find the following values for f x sin I f x Based on these values lim sin I 0 7 0 0 0181 Olim sin 2 0 7 0 73354562801787 Olim sin 1 0 7 Be sure your computing device is set to RADIAN mod does not exist 0 00191 0 000103
Calculus
Limits & Continuity
Suppose lim f x 8 and lim g x 6 Find 24 7 24 7 lim 6 x 7 x 3g x 3g x 4x 4
Calculus
Limits & Continuity
Find the following values for f x sin X f x Be sure your computing device is set to RADIAN mode 0 1 0 01 0 001 Based on the values it appears lim f x I 0
Calculus
Limits & Continuity
Estimate the limit numerically or state that the limit does not exist 4 sin 9x lim 0 sin 8x Be sure your calculator is set in RADIAN mode and give your answer to at least three decimal pla Question Help Video Written Example
Calculus
Limits & Continuity
Find the following Simplify your answers completely f x 6x 7 g x 4 x a f g x b f g x c fg x d f g x What is the domain of f g Enter your answer using interval notation
Calculus
Limits & Continuity
Consider the functions below f x x 1 g x x 1 Find each of the following if possible If it is not possible enter NONE a fog b g f c fog 0
Calculus
Limits & Continuity
Evaluate the function for f x x 3 and g x x 2 f g 9 f g 9
Calculus
Limits & Continuity
The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B whic 65 mi apart When the satellite is on one side of the two stations the angles of elevation at A and B are measured to 87 0 and 84 2 respectively Round your answers to the nearest mile 87 0 84 2 B a How far is the satellite from station 47 1324 mi 0 How high is the satellite above the ground
Calculus
Limits & Continuity
se the graph of h in the given figure to find the following values or state that they do t exist h 2 lim h x X 2 h 6 lim h x X 6 lim h x X 7 Type an integer or a decimal Find h 6 Select the correct choice and if necessary fill in the answer box to complete your choice A h 6 B h 6 is undefined Alim h x X 6 B d Find lim h x Select the correct choice and if necessary fill in the answer box to complete your choice X 6 Type an integer or a decimal Rich x OB The limit does not exist
Calculus
Limits & Continuity
mph of f to complete parts a through 1 If a limit ist explain why 5 answer box if necessary A 1 2 4 Type an integer or a fract OB The value of f 2 is undefir b Find lim f x Select the corre X 2 and fill in the answer box if necess A lim f x 3 X 2 Type an integer or a fractic B The limit does not exist bec defined for all x 2 c Find lim f x Select the correct X 2 and fill in the answer box if necessa OA lim f x X 2 Type an integer or a fractions B The limit does not exist becam defined for all x 2
Calculus
Limits & Continuity
PROBLEM 5 Find values 4p lim 2n 9n 3 9n 1 11448 3p lim 21 n 2 1 1 21 3p n 2 2 2 2 x 4 x 2 Csin