e* + e * — х2 — 2 lim —х sin?x – x2

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

Q: Let S-6x2 + 6z for z 0. According to the alternate form of the definition of the derivative, to…

A:

Q: Let (7z 2x2 for I<0, 8z2 + 7x for r20. f(1) = According to the definition of the derivative, to…

A: Given : Derivative any function is as follows let   f(x)= xm

Q: Express the following limit as a DEFINITE INTEGRAL: lim k= lim =? k=1 n

A:

Q: Find the following limits, using L'Hospital's Rule where appropriate. cos(mx)- cos(nx) (a) lim x-0

A: The objective of the question is find the limit.

Q: Let (7I – 21 for I<0, f(T) = 8, + 71 for z 20. According to the definition of the derivative, to…

A:

Q: Find the limit of the following lim    ln(cos(x)) x→(pi/2)-

A: Consider the given limit.

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (e-X + 5 cos(2x)) x- 00

A: Cosine is a period function,it does not approaches any values as x approaches to infinity.

Q: Use l'Hôpital's Rule to evaluate the limit. COS X lim -X- 3. 3. O A. -3 V3 O B. C. 2 O D. -/2 1.

A: We have to find limit As per guideline we have to solve one

Q: lim,y→0 sin x

A: I am attaching image so that you understand each and every step.

Q: 1) For the function f whose graeh is given the value of each lihmit. If a limit dosent exise enter…

A: From the given graph :

Q: lim 4 sin(x + n) + 3

A:

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

A: A) Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

A:

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

A:

Q: Find the limit of the given functions using a numerical approach 3. lim (2 cos x) 3T 4.

A: The solution of the problem is given in the next step.

Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

A:

Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limits of the function by L'Hospital's rule: limt→∞et+t2et-t If we limits are in…

Q: Find the limit as t-➜0 of r(t)=

A:

Q: Find the limit. 3 - ti + In(t)j k t-3

A:

Q: I/ find the limit of the following: 1- limx cos 2- lim V +x sin

A:

Q: Use l'Hôpital's Rule to find the limit. 5t +t 5t t-0 e lim 4 -t

A:

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: 1. Find the limit of the following functions: x2/3+x-1 lim e x2/3 + cos² x 1- cosx lim- -+0 sin2x

A:

Q: 3t-2 sin t+(e-1) lim +1

A: limt→13t-2sint+et-1t

Q: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) Vx + 5…

A:

Q: C-The result of the following limit is sin t² lim 1-0

A:

Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

A:

Q: Express the limit as an integral (or multiple of an integral) and evaluate.

A: limN→∞3N∑k=0N-110+3kN

Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

A:

Q: Find the limit. (Hint: Let x = 1 / t and find the limit as t→0+.)

A:

Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: 4 Find lim cos C→十0 Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Topic = Limits

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

A:

Q: Q1:- Find the limit for each of the following functions if is exist ? 1) lim|x – 3| x-3 sx + 2 ,…

A: We find limit of given function

Q: Approximate the given limit numerically and verify your answer graphically. VI+4- 2 lim

A: we have the limit  limx→0x+4-2x

Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

A:

Q: Find the limit. -j + sin(5t) k) lim -6t sin?(t)

A:

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

A:

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

A:

Q: Given. lim e = 2e Use only E- & depini tion of a function limit to Prove: e*+1 dx d e?*** 2a+1 ニ2e…

A: epsilon delta ε-δ - definition of limit Let f(x) be a function defined on an open interval around a…

Q: Find the value of the limit lim 01 0 0 O DNE x3 x+0 x³ + x2 < Previous

A: On solving this we will get

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

A:

Q: Find the limit of the following function. а sin (aтz) dz

A:

Q: By using the de finitionof the limit, prove thal (D Lim x (x+1)=D0 e) Linx cos= o

A: Let f(x) be a function defined in the open interval a,b and let c be a point in the interval a,b…

Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

A: We need to find limit.

Q: Find the limit. (e-2x cos(x) lim

A: