(a) | Show that tan- z = in() = n 1, і —z i + z -In i - z -In z +i %3D | - (b) values of tan-(2 + i). ] Use part (a) to find all the

Q: The range of f (x) = cos(tan-1(x)) is: اخترأحد الخیارات a. [-1 , 1] b. (-1 , 1) [c. (0 , 1 (d. [-1…

A:

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

A:

Q: 154. We can obtain a useful linear approximation of the function f(x) - 1/(1 + tan x) at x- O by…

A: The given function is fx=11+tanx

Q: Find all the singularities of tan(z) f(2) = determine their types, and compute the residues at the…

A:

Q: ди ди 1. find az and " if z = 5 tan-1(x)and x eu + In(v) at the point (In2,1) %3D dv

A: Using chain rule.

Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

A:

Q: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

A:

Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: 1 tan 2 1 1 + tan-x +C. 2 2

A:

Q: 2-Consider the function defined by the base i) Find dz (ii) Prove that x дz ?x - дz ду z =…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: y = In O it Vsin 0 cos 0 1+2 ln 0 4 0(21n0) In (YS [cot 0-tan 0 another answer 1 1 [cot…

A: Given

Q: ution t= tan 2 tan). os(x)

A: We have to choose the correct answer from the given option

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: 1 -dx 2-cos(x) Evaluate Select one: O arctan (/3 tan()) + C arctan (V3 tan())+C 2 O arctan…

A:

Q: Antiderivative of sec(3x)tan(3x)

A:

Q: J교+2x +5 글m() + 4| + tan-! C n() ++| - } A x+1 '(***) + c tan-! + C B !In(x + 1) + 시 + tan. x+1 D…

A: Divide and Multiply by 2 . And solve it.

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: 13. Find a primitive function for tan(x). O a) tan (x) +C O b) tan (x) + C O c) cos²(x) + C O d)…

A: To find primitive function for tanx

Q: Evaluate S tan" (x) sec¹x dx. I A tan (+1)(x)tan (-1)(x) + C m+l - 1 I B tan (+3)(x) +tan (+1)(x) +…

A: Let's evaluate given integral.

Q: -1 Let f(x) = tan-¹ e²². Find f" (x).

A: The solution is given below

Q: 5. Find the extrema and the coordinates of the points of inflection for the graph of f (x) = sin?x –…

A:

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

A:

Q: 7) Find all absolute extrema in the function h(x)=cos on the interval (0, 2].

A: h(x)=cos2π3xh'(x)=-sin2π3xddx2π3xh'(x)=-sin2π3x2π3For critical values…

Q: Find the points of inflection,smaller x-value,and larger x -value  of the graph of the function. (If…

A:

Q: f(x) O! f(x)= @ f(x) = f(x) = = # 0 < x < T " , π < x < 2π, and has period 2π 1 1 sin x + sin 3x +…

A: Given -fx=π-x,0&lt;x&lt;π0,π&lt;x&lt;2π,and has period 2π To determine - Fourier series of given…

Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: 116. a. Show that if ƒ is odd on [-a, a], then f(x) dx = 0. -a b. Test the result in part (a) with…

A: a.  Now put

Q: tan(In x) 1. Evaluate: dx A. In cos(In x) + C c.tan?(In x) + C B. In sec(ln x) + C D. tan(In x)² + C

A: The given integral is ∫tan(ln x)xdx

Q: Question#2: Find the linearization L(x) of the functions at each point. (i) : (f(x)) = (sqrt(sin x +…

A: We will find out the required linearisation.

Q: x+y %3D 21. Prove that tan-x + tan-'y tan - xy.

A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

Q: cos e - sin 0 Find a closet rank-1 approximation in the l² norm to A = %3D sin 0 cos 0

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

A:

Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: 38. f(x) = 3(sin-1 x)² %3D 40. f(x) = tan1(Inx) %3D

A:

Q: 7) Find lim (tan(2x))/x= evaluate the values of (tan(2x))/x below. ON ==>"Y=" ==> Y1 = tan(2x)/x ==>…

A: The function is tan(2x)x

Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

A: The  given integral is ∫1-x1+x dx The trigonometric identity is expressed as sin2θ+cos2θ=1 therefore…

Q: Evaluate tan-1 x dx А. 1. tan-x dx = x tan-!x-;In(1+x²) + C В. 1. tan-x dx = x tan-x+;In(1+ x?) + C…

A: As we know that the expression for the integration by parts: ∫udv=u·v-∫v·du Given: I=∫tan-1xdx or…

Q: 1. Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x…

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

Q: A tangent reduction formula Prove that for positive integers n + 1, tan"-x п — 1 tan" x dx tan" -2x…

A: To Determine: A tangent reduction formula find the integral ∫0π4tan3xdx Given: we have reduction…

Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

A:

Q: find Fourier sertes [0, 2w] an O f = X COS X

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

Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: dy - y tan x = 10 tan x dx ution of y(x) using two different techniques. Hint: tan x dx = - In(cos…

A: We have to solve given problem: First method:

Q: 2. Let f (x) = 3 cos(2x) – 1. (a) Find the period and the amplitude. (b) Sketch the graph of the…

A: Use function

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.