Solve the problem. 1) If lim f(x) = L, which of the following expressions are true? x-0 I. lim f(x) does not exist. X-0- lim f(x) does not exist. x-0+ П. III. lim f(x) = L x-0- IV. lim f(x) = L x-0+ A) I and IV only B) I and II only C) III and IV only D) II and III only

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

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

A:

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

Q: 2. Select the best answer below: lim (2x-13 X (-1)* O -2 O does not exist

A: We have to find the limit and select correct option

Q: Evaluate the following limits. 1. lim (1+ Vw)(2– u? + 3w) 22 – x - 2 4. lim 6x2 – 7r +1 7. lim エ→ー1…

A: Topic:- limits

Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4,…

A: Given limit:

Q: V5x+9-3 -lim x+0

A: To evaluate: limx→05x+9-3x which is in 00 form. So, the L'Hopital rule is to apply.

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

A:

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

A:

Q: If f(x)= 2x² +1, then lim S(x)– f(0) is (A) 0 (B) 1 (C) 2 (D) 4 (E) nonexistent OB OD O C O E O A…

A:

Q: Q2) Solve the following limits. 5x+4-2 A) lim X-0 5x+8x? B) lim x-0 3x-16 x2

A:

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

A:

Q: Find the limits x2 - 3x + 2 lim x - 4x as a. x→2+ b. x→-2+ c. x→0 d. x→ 1* e. What, if anything, can…

A: We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

A:

Q: (x+h)³-x³ h C. lim- h-0

A:

Q: Find the value of lim f(r), if f(x)%3D 8r +4 3 z-3+ O 12 O 19 O 34 O 35

A:

Q: Find the limit (1+h)3 –1 lim h h→0

A:

Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

Q: Find the limit. 2 lim 1+ x4 О А. 2 О В. 0о O C. 0 O D. 1

A:

Q: lim X+2 マーX į =

A: We have to do simplification first.

Q: Find the limits 2.1 2x + 3 lim Xo Sx + 7

A: To evaluate the limit: limx→∞2x+35x+7 Solution: limx→∞2x+35x+7 On simplifying further we get:…

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

A:

Q: In(x - 1)2 | 26. lim x→2 In(3 In(x - 1)

A: L=limx→2ln(x-1)^2ln(x-1)

Q: What type of discontinuity is at x = 3, if lim f (x)= o and lim f(x)= oc = 00 x→3 00? x3*

A:

Q: Find the value of Vx+3-/3 lim lim,-5* |x-5|(x²+5) (x-5) 1 O -20 2+/3 O 130 O none О 30 2 V3 O None 1…

A: 1) find the value of limx→0x+3-3x rationalize the numerator limx→0x+3-3x=limx→0x+3-3x×x+3+3x+3+3…

Q: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: Using tables of values, estimate   lim 3x

A:

Q: 5. Given that -3.x2 + 9x – 5 < f(x) < x² – 3x + 4. Find lim,→-3/2 f (x). x2 + 6x + 9 For what values…

A:

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: 2. Find the following limits algebraically. Then support your conclusion numerically. x² – 3x – 10…

A:

Q: lyfical of the itemrs need to be factored or rationalied for the limits to exist) - 1. lim (x - 2r)…

A: given,        3.  limx→-4x+42x2-164.  limx→-33x2+2x-1x2+3x+2

Q: V1+3x-1 lim Answer: 1 %3D

A:

Q: Q1/ Find the following limits. 1. lim x*+3x-4 2. lim x*- 16 x-1 2 X+2

A:

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

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: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

A:

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: If f(x) = 4" , then lim %3D (A) 4 (B) ! 1.

A: f(x)=4xlimx→0f(x)-f(0)x-0=limx→04x-40x=00, indeterminate form. Apply l'hospital rule to simplify

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

A:

Q: Evaluate the given limits: a) 2x3 + 5x² + x – 1 lim x→+0 e2x -

A:

Q: Find the value of lim f(x), if f(x): I6+ S8x +5 6 %3D O 52 О 16 O 20 О 32 O 10

A:

Q: if x 2 Find the value of c such that lim f(x) exists. x→2

A:

Q: 1. Evaluate the following limits. x² + 3x+ 2 lim, →-1 x' +4x +3 2 а. х? — 2х lim,→2 b. Vx? +5 – 3

A:

Q: Evaluate the following limits: 5x +3 lim lim 3h –5 e h→0 a b x→3 x-1 lim 3x(x+4) x2 2h – h? lim d h

A: In the given question we have to find the given limits.

Q: Given fx) ={ax + b (2x – 6 if xs -2 if - 2<x < 2 if 2 sx 2. Find the values of a and h such that lim…

A:

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is