| sin x| | sin x| а. lim b. lim x→0 sin x x→0+ sin x

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

A:

Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

A:

Q: f(x) = { cos x, xpi  which lim does not exist

A:

Q: x(cos(x) – 1), x0 sin(x) – x Evaluate: lim-

A: It is given that,  limx→0xcosx-1sinx-x We have to evaluate it.

Q: sin x 3. lim -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) x-2 4. lim x2+x-6 X-1 0.9 0.99 0.999 1 1.001 1.01…

A: To find limx→0sin(x)x numerically. Find the f(x) values for each x value using function f(x)=sinxx.…

Q: cos x dx - In (1 +x) 1- cos x a) b) lim

A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

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

A:

Q: 1-cos2 (x+y) 3. lim (xy)-(0,0) (r+y>)ety

A:

Q: im xto1 of the function e(2^x) /(x^2) .. use L'Hoptial's Rule

A: Given information: limx→1e2xx2 The objective is to evaluate the limit by using L'Hopital's rule.

Q: cos x ln(x - *) *-+ In (e-e*) 6. lim

A: Topic:- limits calculus

Q: 1. lim cot-1 (e*). 2. lim sech (ln x) x-0 S(x) = sech z

A:

Q: f(x+h)-f(x) For f(x) = V5x +I, find f '(x) using the definition f '(x) = lim - h-0 f '(x) = Using…

A: use the given definition to determine f'(x):

Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = –3 4. lim f(x) = +o, 3. lim f(x) = -2, lim…

A:

Q: lim x approaches 0 ................ (x^2 - 1)(2 - cos x)

A: To find the limit of the function as x approaches 0, the function is given as follows: x2-12-cos x

Q: sin 3y cot 5y Q7// Evaluate limy-0 y cot 4y

A:

Q: Q 3/ x-sin x A- Find lim,0 1-cos x.

A: Explanation and solutions is given below....

Q: sin 3y cot 5y Q7// Evaluate limy→o° y cot 4y

A:

Q: Find the limit

A:

Q: f(x) estinal ? Vx + 1- 1 6. lim -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) sin x 7. lim

A: G

Q: x-sin x' A- Find limx-0 1-cos x.

A: We will apply the L'hospitals rule because the limit is of 0/0 form.

Q: ขน lim (x,y) → (0,0) x² +10y²

A:

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: (r +1)' sin x (c) lim - 2.x X-0 sin x (d) lim- X-0 20' lim + sin 0 (e) 40

A: According to our guidelines we can answer only three subparts. Kindly repost the otherquestions in…

Q: e-3sin z (c) lim x² (d) lim sin(rx) lIn (x – 1) x→1+

A: The given limit is: (c) limx→∞e-3sinxx2  To find the value of the limit.

Q: lim (SC - S(T)) where f(x) = -x²+x+6 f(7+h)-f(7) h h→0

A: f(x)=-x2+x+6= limh→0 f(7+h)-f(7)h limh→0 -(7+h)2+(7+h)+6-[-72+7+6]h limh→0…

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

A:

Q: Find the limits

A: Find the limit limx→-πx+4cosx+π

Q: 3 lim z? sin(-

A:

Q: (b) lim (e) lim x-0* V4+ Vx-1 x+sin x (h) lim X0 x+ cOS X x+sinx (k) lim [x] (n) lim X3 X

A: Limits questions

Q: Rewrite the following as one-sided limits as in Exercise 50 and evaluate.

A: To evaluate the limit. (a).…

Q: tan ( xy) lim 2. (x,y)→(0,1) x´y+ x (a) 0 (b) (c) (d) (e) 1 -/4 -3 || -12

A: This question is related to Differential Equations.

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

Q: 2²+ cos(x) x 0

A:

Q: cos (x + h) – cos x f'(x) = lim h0 57. h cos x cos h – sin x sin h – cos x lim h sin h cos h = lim (…

A: Given: f'x=limh→0cosx+h-cosxh

Q: Lim Cos t X-2SM X2

A: limx→2cosπxx-2sinπx

Q: lim as x approaches 0   x sin(x)/1-cos(x)

A:

Q: 1-cos (x-T) lim x→T(x-T)sin (x-π)

A: Given limit, limx→π1-cosx-πx-πsinx-π

Q: lim -Vx + e* + sin(x)cos(x) 1+ In (x)

A: limx→3-x5+ex1+ln(x)+sin(x)cos(x)=-35+e31+ln(3)+sin(3)cos(3)

Q: c) lim x-+0 tan 3x 1- Jx e) lim x 1-x g) lim(\n² +1-n)

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: 2 cosh 2, 2 0. Then the lim f(x)

A: Given function is fx=2coshx , x&lt;0sinhx  , x≥0

Q: tan( xy ) lim (x,y)→(0,1) x´y+x 2 |3|

A: Given function is limx,y→0,1tanxyx2y+x

Q: ¶/x x-0 sin (1 /x) Lim

A: To evaluate: limx→∞π/xsin(π/x)

Q: 4+ sin x d. lim - 1- i cos(x+x) +2 g. lim

A: To find out the limit, substitute 0 for x and find out the limit value

Q: Find the limits

A: Given,                     lim(x,y)→(0,ln2)ex-y     And we have to find its limit.

Q: not exist". x2 + 3x + 2 (а) lim x-2 x +2 cos O 1 (b) lim 0→0 sin 0 (c) lim In(sin r)

A: To evaluate the following limits: a limx→-2x2+3x+2x+2 blimθ→01-cosθsinθ climx→π+In sinx

Q: 1 lim (x,y)¬(0,0) xy sin x² + y=

A: The limit of the function is given as, limx,y→0,0xysin1x2+y2. To determine the limit of the function…

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

A:

Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A:

Q: 2x e* –1 lim- x→0 sin (2x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…