a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x< 55-px if x 2 5, "p" is any constant and also find the value of "p" assuming that limx>5 f(x) exists.

Q: Show that lim(5x+2)=-18 x-> -4

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: b. Find lim (xv (xVx²+1-x²)

A:

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

A:

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: x* +x² – 1 limx→c x²+5

A:

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

A:

Q: 1. Find the value of the expression lim x²+x+21 X-3 x-1

A:

Q: (3x2 3x2 4. lim x00 x--1 x+1 А. 1 B. Undefined. С. 1/2 D. -00

A:

Q: 5x' +8x² lim x→0 3x* – 16 r? 3

A: Cancel out the common factor from numerator and denominator than put the x and calculate limit.

Q: x6 – 3,000x5 lim x→-0 4x° + 10,000 9

A:

Q: Find Lim f(x) = 2√x

A: Given function: fx=2x

Q: Evaluate lim h→0 1 2 5 (x+h) ² 2h 1 5x²

A:

Q: Calculate lim X→-2 x³ + 2x² - 1 5 - 3x

A:

Q: x*+x3 2. Calculate lim x→0 12x3+128

A: limx→∞x4+x312x3+128

Q: b. Find lim (xvx²+1-x²)

A: Here, we take common x.then multiply denominator and numerator by √(x^2+1)+x

Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: If 3x – 2 s f(x) sx² - 3x + 7 for x2 0, find lim f(x). x-3

A:

Q: Find lim h-0 f(5+h)-f(5) h if f(x) = -2x-1.

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Q: lim (1 – 3x² )= x-2 а. -13 b. 11 С. 13 d. -11

A: By the linearity of limit of a function we can solve the given problem

Q: lim x>-3- x² +2xr-3 a. X- 7X b. lim x>-3+ x2 +2x-3 lim x>-3 x² +2x-3 C. X- ,X

A:

Q: d. lim f(x) %D X-3-

A: