sin(x) * x - lerror| < 0.0000001)

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

A: Given: limx→∞xcos1x

Q: lim (1-cos x1/2) / ln(1+x) ? x--&gt;0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: 2 (sin -'x)²dx Evaluate the integral [(sin -'x) dx V1-x

A:

Q: lim x approaches zero, sin4x/sin3x

A: Given,

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

A:

Q: sin x cos 4x 32) lim X0 X+X cos 5x

A: Consider the given limit

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

Q: 3 lim 2 x2.tan=.sin- X-00

A: We have to evaluate limx→−∞x2⋅tan2x⋅sin3x It can be written as…

Q: 2 sin(-2 x) lim ثم أختر الاجابة ال 0.3) d x-0 4 sin (5 x)

A:

Q: 1. lim sin -;). x→2

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: lim x----->0    sin x sin 2x/1- cos x

A: Given:-  limx→0  sinx  sin2x1-cosxTo find:-     value  of the above limit.Concept:-  Use 'L Hospital…

Q: 3. Consider the function f (x) = sin² x + sin x on the interval (0,2n). a) Find the open interval on…

A: The given function is fx=sin2x+sinx on the interval 0,2π. a) Obtain the first derivative of the…

Q: Q5/ * lim (x-3)(sin-'(x) – x) using L Hopital Rule

A:

Q: SIn (-x) In x if x 0

A:

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: (sin æ)(1 – cos æ) lim COs x x→0 x2

A:

Q: 1. sin (-x)(sin(-x) + 1)

A: Given; Sin(-x)[Sin(-x)+1].

Q: lim cos2x-1/sinx x-> 0

A:

Q: sinh x + cosh x)ª= e4x

A:

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

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A:

Q: 2 |-cos X lim b. X - Sin x

A:

Q: limit x to infinity (1+sin(3/x))^x

A:

Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

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A:

Q: 1- COs x lim x→0 3x sin x

A: This question is based on limits.

Q: Limit as x approaches 0 of Sin(5x)/(2x

A: Limit as x approaches 0 of Sin(5x)/(2x

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

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

A:

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

A:

Q: (Sin X-cos X)^2=1-sin 2x

A: Formulae to note: (a-b)2=a2+b2-2ab. 2 sin x cos x=sin2x. Sin2x+Cos2x=1.

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A: This question is based on Trigonometric Formulas to simplify question.

Q: 6 lim Sinx ex -1

A:

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: lim x→0 (sin3x sin5x/x2) *without use of deritivatives or l'hospital's rule*

A: See the details solution in below

Q: 2 sin(x)-sin(2x) х-sin(x) lim X→0

A: Given,           limx→02sinx-sin2xx-sinx

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A: Introduction: So, according to L'Hospital's Rule, if we have an indeterminate form 00 or ∞∞, all we…

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A:

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Q: tanx – lim 0 Cos[1 – –

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Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

A:

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: sin 2x (c) Determine whether the improper integral dr converges or diverges. If V1- cos 2.x it…

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Q: imit x to infinity sin3x/2x

A:

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.