Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: x +1 lim Vx2 + 2x +3

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: Find the limits: Vx – 1 lim x→1 x - 1 а.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: What is lim1 f (x) ? X

A: Find your answer below

Q: Evaluate the limit V5 +3r2 lim 5 6x

A: We find limit of given function

Q: Use the Squeeze Theorem to find limx→c f(x).

A: Given that 4-x2≤f(x)≤4+x2 To find the limit of the function using the Squeeze theorem when x→c=0.

Q: Find the limits in Exercise

A: To evaluate: limx→5-3x2x+10 Solution: limx→5-3x2x+10 On simplifying further we get:…

Q: Use l’Hospital’s rule where applicable to find the limit.

A: the given limit is: limx→08x6+3x4-9x9x7-2x4+x3 we have to evaluate the given limit.

Q: - Find the limit lim Xo 2x-3

A:

Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

A:

Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

A:

Q: Q4: Find the following limits if exist:-- x-1 x2-x 1) limx-1²+2x-3 2) limx-1 x²+3-2

A:

Q: x³ - 8x* +1x lim xa -5-14

A: Dear student our policy is to answer first one only in case of multiple question kindly repost the…

Q: Use l'Hôpital's rule to find the limits in Exercises 5x - 2r - 8x2 11. lim 7x + 3 12. lim x 12r + 5x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the limits in Exercise

A: Given limx→∞x-34x2+25.

Q: r+ 2 Calculate the limit lim 1-2 x2 – 3x – 10°

A: By using L'hopital's rule, we find the limit of the function.

Q: Find the limit. 3x + 5 lim x→0 x - 4

A: Find the limit  limx→∞3x+5x-4

Q: Use the Squeeze Theorem to find lim f (x), given that 2 - |- 8| < f(1) < 2+ |r – 8|.

A:

Q: x² + x lim * + 2x + x³

A:

Q: If −x2 − x + 1 ≤ g(x) ≤ x2 − x + 1 for all x does not =0, what is lim x→0 g(x)?

A:

Q: Evaluate the limit: -V4+x² lim X→0- x2

A: limx→0--4+x2x2

Q: Evaluate the limit: 6x 12 lim I> 2 r2 + 3x 10

A:

Q: Q3: (a) find the following limits if exist:- (1) limx-o √x+9-3 1-cosx xsinx (2) limx-07 (3) limx-1…

A: Topic = Limits

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: Estimate the limit numerically. 3x² +270x+5 lim 2x+15 + oo

A:

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Find the Limiti lim (xt +2x") メ→ -○

A: Solution is given below

Q: Use L'Hospital rule to find the limit. lim (Væ2 – 6x – x) -

A:

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

A:

Q: lim f(x) = 81 (a) VF(x) (b) [3f(x)] (c) [f{x)]²

A: Using rules of limits.

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: If 2x 0, use the Squeeze Theorem to find lim g(x).

A: Given that : as per squeeze theorem

Q: V x2 + 9 - 5 lim X→-4 x + 4

A:

Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

A:

Q: Find the limit. -7x + 5 lim Vx2 + x X→-0

A: Given limit, limx→-∞-7x+5x2+x

Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

A:

Q: Evaluate the limit 2x + 4 lim I→ 0 3x2 - 7x + 7

A: Given

Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: if Væ² – 5x – 6 < f(x) – 1 < v6² – x² then find lim f (x) - | - x-6

A: Given:x2 - 5x -6  ≤ f(x) -1 ≤ 62 - x2To find : limx→6f(x)

Q: Use continuity to evaluate the limit. lim In(2 + V1 + x)

A:

Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

A:

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

A:

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

A:

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.