sin 2x B) Find: limx→0 2x2+ x

Q: What is lim Sináx, cosx А. 0 В. 6 С. 1 D. Ø (DNE) Ø (DNE)

A:

Q: 4x³ + sin x lim 2x3 + 3

A: Given : limx→∞4x3+sinx2x3+3

Q: Evaluate using Theorem as necessary.

A: Given : The limit is limt→0 sin2tt .

Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

A:

Q: Evaluate limx-->0 (sin 2x sin 9x)/(x^2) Without using L'Hospital's rule.

A: The given function is limx-->0 (sin 2x sin 9x)/(x^2)Use the expansion for sin x to simplify (sin…

Q: What is lim m→0 sin(m) m ?

A:

Q: lim x-->0 (sin(2x^3))/(3x^2)

A:

Q: Find tant r lim t

A:

Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: prove that lim (2X+iy2)=D4i %3D

A: We have to Show given expression of Complex limit.

Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: Evaluate using Theorem as necessary.

A: The given is the symbol of limits, hence the definition of limits helps to find the required. A…

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

Q: Evaluate limx-->0 (tan 9x)/(sin 4x) Without using L'Hospital's rule.

A: Obtain the limit without using L’Hospital rule as follows.

Q: Evaluate sin 0 – 1 lim 0 - T/2 In sin 0

A:

Q: lim »0 sin(2t) tan(7t) is t2

A: Here we find the value limt→0sin(2t) tan(7t)t2

Q: Evaluate using substitution.

A:

Q: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

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: 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 a sin(1/2),

A: Given,           limx→0xsin1x

Q: sin x lim bx = ? Use L'Hospital's Rule

A:

Q: 1 Lim x→0* x0x 1 sin x

A:

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: lim sin(1/r),

A: We have to find limit

Q: Find the limit of the trigonometric function.

A: Given:limx→0 sec2x

Q: sec(x) – sec(a) lim x - a

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the Oimits :- sin 3y Lim Sin Jz8 Lim My JzO ot

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

Q: Find the two limits: sin 2x lim r-T/2 COS x

A:

Q: 3 lim z? sin(-

A:

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

A:

Q: Prove that lim sin( nx) + n dx= In 2 . (n+) Explain your answer carefully

A:

Q: Evaluate using substitution.

A: We have to calculate the following limit L:

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: Evaluate limt--&gt;0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: sin z coS T Q1-Solve by hospital rule lim

A:

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

A:

Q: Prove lim sin (t)

A:

Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: Evaluate using Theorem 2 as necessary.

A:

Q: Let a > 0 be a real number. Prove that lim x“ sin = 0.

A:

Q: Find the value of limx→0 sin(sin x)/x

A: L'Hospital Rule: According to this rule limit of the intermediate form 00  or  ∞∞ can be solved by…

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Evaluate:- x+2 sin x 1: lim Vx +2 sin x +1-Vsin? 40 einf

A: Since you have asked multiple questions in single request.so we will answering only first question.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.