4. ( sin(x)+1 x 05x+e+(x−1)² a. lim b. lim x-0 c. lim x-1 tan(-x) 2x sec(x + 4) = √2x+2-2 1-√√√x > Compute the following limits =

Q: x, x 2. y=h(x) 4 3 y-2 Show that a. lim h(x) + 4 b. lim h(x) + 3 c. lim h(x) + 2 X-2

A: Given, h(x)=x3,  x<23,  x=2  2,   x>2 now show the limit on x→2…

Q: lim sin(x)d.x (x2 + e2)2

A:

Q: tan(sin(ra)) tan(т(»—100)) Find lim

A: The objective is to evaluate the limit.

Q: (7) Lim x= 1/2 X- X COS X TT- 2X

A: Since you have posted multiple questions and we will provide the solution only to the first question…

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: The limits of the following two expressions are: 1 1 3. x' +x-6 (a) lim x-3 3+x (b) lim x2 x-2 A.…

A:

Q: lim x→0 x⁹⁹ sin (7x) (sin x) 100

A:

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: C2. SOLVE STEP BY STEP IN DIGITAL FORMAT Calculate the limit of the function (I HOPITAL) sin(2x) lim…

A: Explanation of the answer is as follows

Q: Find lim Sin (X+2) X->2 x4x-2

A: Explained below

Q: lim¸ √x³ +8-3 x+1 7. Evaluate x→-1 8. Use a table of values to find an approximate value of limx→…

A:

Q: 2. 2. COS X Sinx lim 4x-X

A:

Q: 1) lim X-2 2x-4n x(1-cosx) 2) lim х-0 tan(tan?x)

A:

Q: 2x x-0 sin 1x f. lim

A:

Q: 3x4-x2 2) x"m. (2 + inx) lim lim 1) x4-1

A:

Q: 3. Find the limit. tan(5x) 0 sin(3x) sin(6x) (2) lim x04x-5x (1) lim

A:

Q: x+1-cos²(x) 3sin(x) 7. Find lim

A:

Q: Lim x tends to pi/4- (LHL) √(1-√sin2x)/(pi - 4x)

A:

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: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

A:

Q: Find x² lim x0 1 - cos x

A: Solved below...

Q: V3r-1 7. lim X- sin? x-cos(2x)

A:

Q: 1. lim )Gt h->0 2. lim xZ X-1 X>( X-I

A: here is the solution

Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: 2.r + x sin 3.x 1. lim * 5x - 2x +1

A: Here we find limit

Q: olve

A: Given : The limit , limx→0 1x sin x - 1x2

Q: tan(31x) lim x → 0 5x

A:

Q: 1. lim (2r + 5) 2. lim (10 3x) X12 3. lim(-x + 5xr 2) 4. im (x'-2r? + 4x + 8) 5. lim 8(t - 5)(t-7)…

A: