1 lim X→0 In(1+x) 1 Arctanx

Q: Only one of these calculations is correct to evaluate the definite integral xe-X dx Select one: lim…

A: Explanation of the answer is as follows

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

A: Let's solve for given limit.

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: 1- cos X lim x→0 1- Prove that

A: As per Bartleby's expert answering policy, we cannot answer more than one question so kindly post…

Q: 1 Use l'Hopital's rule to evaluate lim 1+0+ \I In(1 + x),

A: Question is solved.

Q: lim sin (-2 T x) = x → -3

A:

Q: Use L'H to find the limit at x \arrow 0: arctan(5x)/x   x-->0

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Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

A:

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

A:

Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

A: Explained below

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: 1 O Use l'Hopital's rule to evaluate lim x+0+ \x In(1+ x)

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

A:

Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: by L'Hopital's rule 1-cos(x) lim x2

A:

Q: 2) lim 1-cos (2 arc sinx) In(a+x2) calaulate the limit.

A: Solve the limit limx→01-cos2arcsinx1n1+x2

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

A:

Q: 9. Build a table to estimate lim sin (Hint: Use multiples of T) X-0

A: Given: To Find:   A table to estimate the value for the given function.

Q: 12. Evaluate the limit ,kT. lim -> sin(-) n→∞ N n k=1 by expressing it as an integral.

A:

Q: Prove the limit using epsilon/ delta.

A: To prove the statement by using epsilon, delta definition of a limit is,

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: -e lim te Int - 1

A:

Q: Compute lim 2>0 sin x O 2 O-1 1 undefined

A:

Q: 02.) Find the limit lim X+x cos X sin x cos x 1- X→0 lim sin 5x SIn 4x 3-

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Q: 1 Lim x→0* x0x 1 sin x

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Q: Q. Prove that: Lim tanhx =1 .

A:

Q: Use : L'Hospiral's Rule lim In x X-o ot cot x

A: We have to find limit of given function.

Q: TD - xs3もーな x sin"x Lim ×→の

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Q: 3 (e) lim (1 x2

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Q: 1 Use l'Hopital's rule to evaluate lim I+0+ In(1+x)

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Q: use Series to evaluale lim sinhx²- x 2 メー→ メ Cos x 3.

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Q: Find lim (e-2x cos x) (Hint: Squeeze Theor

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Q: Find the following limits. used L'Hopital's rule  lim   (1-2x)1/x ?→0+

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Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

A:

Q: I. Evaluate the following limits: sinh(x2−x2) 1. lim x→0 sinh(x−x) 2. lim (x - ln x)* x+0+

A: The given problem is to evaluate the given limits of the given functions by checking the left hand…

Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

A:

Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

A:

Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: Compute limx→0 sin(x) − x / x^3

A: To find the limit, simplify the expression and then apply the limit to each term in the expression.…

Q: arctan (2x 7. A) Compute lim arcsin (3x)

A:

Q: 4. lim In(cosx) 2

A: Given limit, limx→π2-ln(cos x)

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.