4. Given there exists a function h(x) such that 2x³ + 5 < h(x) < xª + 5 for all r near 2, h(x) +3 find lim x→2 4

Q: x3-9x 2x+6 8) Let f(x) = lim X→ -3 Enter your answer as either "yes" or "no" or "does not exist".…

A:

Q: 3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): а. x-0-…

A:

Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

Q: (2) Use the definition of limit of a function to find lim x³-3x-2 x+2x2 - 3x+2

A: To find the limit of the function x3−3x−2x2−3x+2 as x approaches 2, it can apply the definition of…

Q: Vx-2 lim х-2+ Vx2-4

A:

Q: 5. Sketch the graph of one function y = f(x) that satisfies all of the requir- ments below. lim f(x)…

A:

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: |x + 2 x + 2 17. а. lim (x + 3) b. lim (x + 3) x→-2+ x + 2 x→-2 x + 2

A:

Q: Find lim f(x) if, for all x > 1, x →∞ 12ex - 21 4ex < f(x) < 3√x VX-1

A:

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

A:

Q: Let f(x) = a² + 3. Find lim * + h) – f(x) h→0 h Select one: O a. 0 O b. 3 O c. 2x+3 O d. 2x

A:

Q: 2. Evaluate lim,.

A: (1) Consider the provided limit, limx→91x-191x-9 Find the limit of the above expression. Simplify…

Q: If lim f(x) = 4, what can you say about ƒ(1)? x-1

A:

Q: If lim f(x) = 8 and f(7) = 3, then lim (4f(2x + 1)) = %3D %3D x→7

A:

Q: b) Evaluate lim g(x) if 2x − 1 ≤ g(x) ≤ x² − 2x + 3 x→2

A: Above question is solved.

Q: Find the value of lim f(x), if x→7+ S8x + 2 x 7 f(æ) = 45 9. O 16 O 87 O 57

A:

Q: Find lim f(x) if x →∞ 4x - 1 X f(x) 5.

A:

Q: Q2: Find the limit x + 3 lim x→-3 x2 + 4x + 3

A: We have to find limit

Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

A: E

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

Q: Find the value of a so that √x²-5x = 4 Vx2 lim √x² + ax - X18

A: We are required to find the value of a for which limx→∞x2+ax-x2-5x=4

Q: (A) (B) ƒ(5) - ƒ(3) 5-3 f(3 +h)-f(3) h (C) lim h→0 || f(3+h)-f(3) h

A:

Q: Evaluate: 1. lim [√x² + x − √x² + 4] = X→ +∞ 2. lim [(x²-In(x + 1)) cotx] -0-x

A: