Q3: (a) find the following limits if exist:- (1) limx-o √x+9-3 1-cosx xsinx (2) limx-07 (3) limx-1 x²+3x-4 x-1

Q: 2x-5 lim 3-5x+x² I3D

A:

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: xV1-3x lim | V1-4x3 I-00 %3D

A: Suppose L is limit value of given Limt

Q: lim, 6 8(x – 5)(x – 7) Answer: -8 4x2-9 lim3/2 2x+3 Answer: 0

A: The value of the given limits are –8 and 0 respectively.

Q: x²-4x+4 1. Find lim- 2 x+x-6

A: Part 1,

Q: 6х2+1 2. Find lim X→0 V4x4+3x+1

A:

Q: -e g). lim [In(6x² + 5) – In(3x² – 6)] h). lim ズ→の

A: g) limx→∞ln6x2+5-ln3x2-6h) limx→-∞e2x-e-2xe2x+e-2x

Q: 2. Find lim (√x + 2 = √2).

A:

Q: Q2: Find: 3-8 b)lim 8-2x a) lim x-2 5-Vx2+9 x-2 x-16

A: There are some forms in mathematics which cannot be determined. These values are still not known;…

Q: Find the following: x/3 + 9x/5 i. Lim X 06x1/2- 4x1/4

A:

Q: 25) Find: lim,(x²+ax - √x² + bx).

A:

Q: 2. Find lim 7x+5

A: limx→∞7x+5x2-4x=limx→∞x(7+5x)x2(1-4x)=limx→∞(7+5x)x(1-4x)

Q: vertical

A:

Q: Ex: Find lim, 3f(x) if f(x)%3D x-1 13x-7 x > 3

A:

Q: Vx² +4 - 2 Find lim x->0

A: Consider the given limit limx→0x2+4-2x So, limx→0x2+4-2x=00   Apply L'Hospital's rule:…

Q: Find the limits of the functions lim メ>- (6lim x 2. xペー 2x+4

A:

Q: x2 + 8x + 15 if x 2. Find lim f(x). x-2+

A:

Q: Find lim,x - Vx²+ 2

A: To find the limit

Q: 2r – 5x²/x Find lim x5/2 – 3x +1 — Зх + 1 X- 00

A:

Q: √x-10 lim x-100 x-100 lim x→4 2 x² - 2x-8 x² -16

A:

Q: Q.2 Find the lim, 2x-6|

A: Given, limx→3 2x-6

Q: Find the following: x1/3 + 9x1/5 i. Lim x-0 6x1/2 – 4x1/4

A:

Q: Vx² + 5 – 3 lim Find x² – 4 x2

A: To find the limit: limx→2x2+5-3x2-4 Solution: It is 00 form. So, we we will use L-hospital rule. In…

Q: 3 Find x=x-12 lim. x-7-3 x2+ 8x+15)

A:

Q: Given the function h, find functions f and g such that h(x) = (go f)(x). h(x) = (6+ 4x)" a. f(x) =…

A:

Q: V2 x4-625 Find lim→5 5 х-5 O 1200/2 O None O 100/2 O 86/3

A:

Q: Find domain, range, asymptote, yintercept, and xintercept for f(x)=In(x+3)+3

A: Given: f(x)=In(x+3)+3 To find domain, range, asymptote, y- intercept and x- intercept.

Q: x2 - 7x + 12 Explain why lim xS3 lim 1x xS3 42 and then evaluate х - 3 x2 - 7x + 12 lim xS3 х — 3

A: The given limit is:   limx→3x2-7x+12x-3 To show that, limx→3x2-7x+12x-3=limx→3x-4, factorize the…

Q: Find the following: x1/3 + 9x1/5 (2х — 1)1/2 — 3 - i. Lim 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

A:

Q: Find the following: x1/3 + 9x1/5 i. Lim х-0 6х1/2 — 4х1/4 ii. Lim х+5+ (2х — 1)1/2 — 3 х — 5

A: