3. Find the indicated limits. if x < 2 if x > 2 f(x) -2+ 4x – x² a) lim f(x) x→2+ b) lim f(x) x→2- c) lim f (x) x→2

Q: Find the indicated limit given that lim f(x) = 5 and lim g(x) = 4. xa lim [2f(x) – 4g(x)]

A:

Q: 3. Explain why the following limits do not exist. 1 (a) lim x-5 (x-5)2 -x² +3, (b) lim h(x), where…

A: (a) limx→51(x-5)2 Let  f(x)=1(x-5)2 As x approaches 5, (x-5)2 approaches 0, and so f(x) approaches…

Q: 2/ Find the value of the limit: lim x/*,

A:

Q: Find the limits limx→0+{1 + 1/x}x

A:

Q: 2. Use the definition of the appropriate limit to show (a) lim→∞(2x² + 4x – 1)/(3x³+ 1) = 0. (b)…

A: a) Given limx→∞2x2+4x-13x3+1

Q: Prove from the precise definition of a limit: lim x = 4 x-2

A: We have to solve the limit using definition.

Q: lim (4.x – 3) = 9

A: The given limit,      limx→34x-3=9

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: Find a Limit using factoring:

A: We have to find the limit using factoring: limx→1x2+2x-3x-1 This is 00 indeterminate form of limit.…

Q: Find the limit. lim (Váx + 6 + 1)

A: The given limit is limx→56x+6+1

Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

A:

Q: 4. lim ) ズ→1 Xー1

A:

Q: x² – 1 lim x→1 x – 1

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: Use l'Hôpital's rule to find the limits x- 2 7. lim X2x - 4 x? - 25 8. lim -s x+ 5

A: l'Hospital rule is used when the value of the function is not defined by directly substituting the…

Q: Find the limit.   Lim  x→1+      x1/1-x

A: Given function is By property of logarithm

Q: Use l’Hôpital’s Rule to find the limits

A:

Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

A:

Q: lim 1-3メ) 2. X->

A:

Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: 1 3) lim (1+ 8x) x→0+

A: Find the limit

Q: Find the limit. lim x2/(1-x) X→1 *

A:

Q: 5x2 + 10x + 1 20. lim x* + x² + 1

A:

Q: Use l’Hôpital’s rule to find the limits

A: Given: limx→π2lncosecxx-π22 for evaluating given limit, in given limit we substitute x=π2+h so,…

Q: 2. If it exists, find lim f(x) where X--1 x =-1 f(x) = { *x– 1)³, x+-1 4, If the limit does not…

A:

Q: Find the limit of lim, 1 f (x) if f (x) = 3 - x, if x +1 and f (x) = 1, if x = 1

A: For the  given statement

Q: Evaluate the given limits numerically (using table of values) and graphically 1. lim2 X-2 x-2 f(x)

A: x 1.9 1.99 1.99 1.999 2.001 2.01 2.11 f(x) 3.9 3.99 3.999 4.001 4.01 4.1 4.11     limx→2x2-4x-2…

Q: Find the indicated limit given that lim f(x) = 2 and lim g(x) = 4. X→a lim [5f(x) – 4g(x)] Xa

A:

Q: 4. Using the precise definition of a limit, prove lim (2x +8) = 38. x-15

A:

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: Find the limit L. Vx - 3 1 lim X 4 X- 4 L =

A: After the substitution of limits the function gives an indeterminate form 00.

Q: Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: a) lim- X- sin x -X…

A: We have to find the limits of the given following conditions

Q: Evaluate the following limits if they exist x +5x-3 a) lim x² + 2x – 6 x² – 3x – 1 b) lim x' +1 c)…

A: In the question we have to calculate the limit of the following functions given.

Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: Determine the following limits at infinity. 4x² + 2x + 3 lim x²

A: Consider the provided expression, limx→∞4x2+2x+3x2 Determine the limit of the expression. First, we…

Q: Find the indicated limit given that lim f(x) = 5 and lim g(x) = 2. lim V3f(x) + 6g(x)

A:

Q: 4. Find the following limits or determine that they do not exist: 1+1/x a. lim,-0 1+1/x² 1+1/x? b.…

A:

Q: lim(4x – 3) = 5 x→2

A:

Q: -x - 4, x 3

A:

Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: 2) Find the following limits if they exist. a) lim xVx* +1-x lim(x+e')% b)

A: We have to find out limit

Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x&lt;-1x+2, x&gt;-1 We have to find the following…

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

A:

Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

A:

Q: (b) Find the following limit: 4x +5 lim x+2 2x -1 (i) (ii) lim 4 x+* x* -x' +2

A: The solution is given as

Q: 2/ Find the limit of the function lim X415 хъ Ч 2 X

A:

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: ) Find the following limits if they exist. 1 lim x→0 x 1

A:

Q: Use a table of values to estimate the value of the limit of x + 4 - 2 lim f(x) f(x)

A: The given limit to be evaluated is limx→0x+4-2x Now to calculate the value of this limit by the…

Q: Find the limit. (- 3m=) lim In x x→0+

A: