# Limits & Continuity Questions and Answers

Calculus

Limits & ContinuityThe 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 & Continuity6 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 & ContinuityThe 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 & ContinuityA 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 & ContinuityCheck all that apply sin 5x sin CT 5 5x 5x sin 6x 5x 6x sin 5x sin 6x 6 sin 5x 6x

Calculus

Limits & ContinuityThe 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 & ContinuityState 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 & ContinuityThe 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 & ContinuityTo 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 & ContinuityThe 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 & ContinuityFind 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 & ContinuityThe 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 & ContinuitySuppose 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 & ContinuityGiven 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 & ContinuityEvaluate the limit 4 6x lim I 11 4x Use oo if the limit is and oo if the limit is

Calculus

Limits & ContinuitySuppose 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 & Continuity3 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 & ContinuityWhat radical function is represented in the graph f x Simplify your answer 9 3 0 4 4 1 5 X

Calculus

Limits & ContinuityFind 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 & Continuity13 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 & ContinuitySketch 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 & ContinuitySuppose 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 & ContinuityEvaluate 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 & Continuity24 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 & ContinuityThe 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 & ContinuitySuppose 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 & ContinuityGiven 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 & Continuity8 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 & ContinuityFind the domain of the function Enter your answer using interval notation g x 4 7x 0

Calculus

Limits & ContinuitySuppose you know that lim f x 16 x 9 Find the following 16 f x lim x 9 f x 4 FA

Calculus

Limits & ContinuityFind 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 & ContinuitySuppose 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 & ContinuityFind 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 & ContinuityEstimate 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 & ContinuityFind 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 & ContinuityConsider 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 & ContinuityThe 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 & Continuityse 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 & Continuitymph 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 & ContinuityPROBLEM 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