Evaluate L = lim(x→0) (e-x-1)1/lnx

Q: evaluate the limit lim x→1+        (ln(x)) / ( ln(x − 1))

A: Given:

Q: Evaluate the limitlimx→0+x (ln(x))^2

A: To determine the value of the limit.

Q: Evaluate lim f(x) where f(x) = x +2 cosx +1 e-4 for x20

A: Use the existence of limit definition

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: Compute x-+xX lim X-700 It Ttx Sinx 2) Lim X-70 CUSX-1 X3-1 1L-X

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

Q: lim at e -

A: Find the limit when x tends to 0

Q: 1S 章テ(メ) H+3x寸hen lim トーつ0

A: the objective is to find the derivative of the given function by using definition of derivative

Q: Find lim eR dt x 00 1/e 1 e

A: We will find first integration then after we apply limit

Q: 18. lim x+oo 3 20. lim log,

A: Given function f(x)=log12 x we write    log10 x=  log x     and we know thhat    log10 10=1

Q: will lim n-00 In(x)dx lim fn(x)dx?

A: Given that, fnx=2n2x;x≤12n2n1-nx;12n<x≤1n0;1n<x where , fnx on 0,1 It is possible to take…

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: III. Use Squeeze Theorem to evaluate lim 8478 COS X log x

A: To Evaluate: limx→+∞cosxlog12x by using squeeze theorem:

Q: Find the integral.

A: Given,

Q: Find the limit. sin 5x lim X0 3x

A:

Q: Evaluate x-y lim In x-ln y where y is a constant

A: L'Hospital's Rule : Suppose  limx→a f(x)g(x) = 00  OR  ∞∞  (indeterminate form) then  limx→a…

Q: Find lim. Sin (X/y X-T/4

A:

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

A:

Q: x2 – 4, x 3 -

A:

Q: t(x)=6x/ ln x 10 What is lim               x →+∞ t(x)?

A: It is given that, the function

Q: lim,-o ([sin x]*) is

A:

Q: 1. Find the limī lim In(sin x) X→π-

A:

Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

A:

Q: d. lim h(x) Preview e. lim h(x) = x→00 Preview f. lim h(x) = 00--x

A:

Q: Estimate the limit by substituting smaller and smaller values of h. 6h lim- h-0 1 - Round your…

A: To evaluate:limh→06h-1h

Q: se L'Hopitals's rule to find lim xIn(e* – 1).

A: Given query is to find the limit of the expression.

Q: Evaluate limx=0+ e(1/x)

A:

Q: TD - xs3もーな x sin"x Lim ×→の

A:

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

A:

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

A:

Q: Find the limit by interpreting the expression as an appropriate derivative. In (e10 + Дӕ) — 10 (а)…

A:

Q: Show using sequences of functions that 2 lim e dx = 0.

A:

Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

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: 2x cos. X 17) lim --

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: Show that lim x sin l/x = 0.                   x→ 0

A: It is known that the absolute value of sine function is not greater than 1, then  -x≤xsin1x≤x

Q: Find the limit as x approaches negative infinity of (xe1/x-x)

A:

Q: find the limit lim as x approaches 0 from the right of (square root of x) / (ln (1+x))

A: We need to evaluate the given limit.limx→0+xln1+x

Q: d. lim+ In 1000 X X5

A:

Q: alignment at x² + x – 1 limx→ 2x2 — х + 1 has a horizontal at???

A: Topic = Limits

Q: Evaluate the limit: sinh x2 – x2 lim x→0 sinhx − x

A:

Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

A:

Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)

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.