1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 cosh(x) cosh(x) + cosh(x) – He* + e*) + e* - o*) e* + e*) - e* - e- II II

Q: Differentiate between regular and isolated singular point. Whether e-xsinx is harmonic or not.

A: A point at which a function f(z) is not analytic, i.e. at which f '(z) does not exist, is called a…

Q: If tanx=sinha prove that a=ln(secx+tanx

A:

Q: Prove the identity.

A: We will use

Q: •sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin…

A: 3) sin2x2=sinx tanx22=sin2x2 4) sin2x=2cos2(x/2)1-cosx=sin2x 5) 2sinx-sin2x/(2sinx+sin2x)=tan2x/2

Q: 2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) –…

A:

Q: 0, 0 <x< A, f(x) ={1, n <x< 2x, sine series, period 6x 2, 2n <x < 3x;

A:

Q: lim x-->0 (1+sinx)^(1/x)

A:

Q: limx>0+ (1/x- 1/tan-1x)

A:

Q: Use partial fractions to evaluate the definite integral. Use a graphing utility to verify your…

A:

Q: ((주)' lim x (1- cos () COs X->- 00

A:

Q: In 2x -dp-

A: To evaluate the integral: ∫2ln2xxdx Solution: Let substitute t=ln2x. Differentiating both sides, we…

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: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

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

A:

Q: = cosx (sinx). 2. Find the Fourier series on -≤x≤π for f(x) =

A: Given the function fx=cosxsin2x, -π≤x≤π

Q: 4 Test for homogeneity fx,y)- tanx- see'x - Osy

A:

Q: Approximate the area under f(x)=3x^2 +1 on [-5,0] using RIGHT Riemann sum with 5 approximating…

A: According to question,Given Function,f(x)=3x2+1,In the interval -5, 0

Q: lim tan 2x tan ax

A: Given that,limx→0tan2xx

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x…

A:

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

A:

Q: First and second derrivative of: x Arctan x-In √x^2 +1=y

A: Given expression: x Arctan x-ln x2+1=y It can be written as follows: x tan-1 x-ln x2+112=yx tan-1…

Q: cosh x sinh x Sin-x cos"x a a*lna tanh x sech x cosech x - cosech x coth x Sinx COSX sech x - sech…

A:

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

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

Q: しx)f erentiate f メて ×ケ-X arcsin (3x -1)+ In (5x*+3) 6arctan (1-x) . メ9 fon

A: f(x) = sin-1(3x-1) + ln(5x4+3)

Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

A:

Q: 1- sin x a) Evaluate the limit by using L’Hopital's rule lim *x→7½ 1+ cos 2x b) Evaluate the…

A: (a) Using L'Hopital's rule, take derivatives of numerator and denominator then simplify it and apply…

Q: f(x) = = x, over the interval - < x < and has period 27 f(x) [cos cosz+cos3z + cos 5 +... f(x)…

A:

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

A:

Q: prove that cosh^2x-sinh^2x=1

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

Q: Formula to evaluate the definite integral. 10 In x dx Use symbolic notation and fractions where…

A:

Q: lim Sinh(x) -X L'Hospitals rule

A: Given:        limx→0sinhx-xx3 L'Hospital rule:    If limx→af(x)=0 and limx→ag(x)=0 then…

Q: simpsons 1/3rd rule when n=2 find integration from 0 to 1 1/√(5-x2)

A: We need to approximate the integral , ∫01 15 - x2 dx Here , n = 2 By using Simpson's 1/3 rule ,  ∫ab…

Q: indefinite integral* (26/(x-1)(x2+25)) dx

A:

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: Finel critical pointof few= un +ln Junt n, also find incred reasing and decreasing funchon given

A: Given function is              f(u)=ueun+lnun+n   ⋯⋯⋯⋯⋯⋯ (1) where n=824 To find the critical point.…

Q: riemann sum from 1 to 4       x^2+x

A: Given x2+x

Q: f(x) = = x, over the interval - 1)=-4 [002-2008 22 +cos 3.- cos 42+...] f(x) 2 [sin zsin 2 J II sin…

A:

Q: limit as x approaches 0 of x^6*cos(4/x)

A:

Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

A:

Q: Simpson Rule. 2- x, (1, 3), n=4 3- x.sin(x), (0, 2), n=6 4- 1/(1+ x³), (0, 1), n=2, 4 ---

A: Since you have post multiple questions, according to our guideline we can solve only first one, or…

Q: Approximate sin 49º by Taylor series

A: We know that,  49°  = 45° + 4°  = (π/4 + π/45) rad = (45+4)*π/180 =  49π/180 rad

Q: x+13 dx х+4

A: 1) Evaluate: ∫3x2+14x+13x+4dx

Q: tan(x)-sin(x) e. lim x2 tan(x) (In (cos(3x))] f. lim 2x2 tan(x)-x g. lim x0 (sin(x)-x. ex-In(1+x)-1…

A: e) Given data:   The expression for the given limit is limx→0tan(x)-sin(x)x2tan(x).     The given…

Q: Find delta value for the limit of x-->0 of tan5x/sinx when epsilon = 0.1

A: Introduction: The limit of a real-valued function is the base of differential calculus. A single…

Q: (1) limx→(π/2)-(tan x) (2) limx→0 x ³(tan-¹ x - x)

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