(x²–1)dx (x2 – (x*+3x² +1)[tan-1 The evaluation of is In |tan-1| + e -In |tan-| + c (i) (ii) (iii) None of these

Q: The domain of the function f(x) = cos-¹(e) is O(-00, 1] O(-∞0,0] O(-∞o, In(cos 1)] ○ [0,00) O[-1,1]

A:

Q: an = bn || ["*(8a² + 7a) cos(nra/2) da (8x² + 7x) sin(nπx/2) + 2 NT 128 n²π7² 12112 +4 ["* (8x² +…

A: In this question, student asked to explain steps in existing answers. We, briefly discuss these…

Q: Evaluate f{ [sec (x) + csc (x)] + sin ()} dx : (2)]? + sin (팔프)}dz O a. tan (x) In |csc (2æ) + cot…

A: To solve the following integral

Q: What is the range of the function f(x) = 2 cos x + 1? [0,3] O[-2,2] O[-2, 1] O[-3,0] O[-1,3]

A: f(x)=2cosx+1

Q: Evaluate the integral ftan¹ (x)sec (x) dx . O sec³(x) 5 O O tans (T) 5 O O None of these tan³ (x) 5…

A: find which method is use for integration.

Q: f(x) = -2sin(x) Amplitude: f(x) = -3cos(x) Amplitude: f(x) = 6sin(x) f(x) = 10cos(x) %3D Amplitude:…

A: If f(x) = Asin(mt + n) or f(x) = Acos(mt + n) then amplitude = |A|

Q: Evaluate the integral [ 3 sec(x) tan(x)dx O 3sec(x) + C 3tan(x) + C O 3sec(x)tan(x) + C O None of…

A:

Q: x2 1+x2 x3 3 + C x+ x3 3 Ox- In (1 + x²) + C Ox – tan-1 (x) + C X - O In (1 + x²) + C

A: We have to find the indefinite integral

Q: (a) | Show that tan- z = in() = n 1, і —z i + z -In i - z -In z +i %3D | - (b) values of tan-(2 +…

A: This is related to Complex Analysis

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: g(æ) + x sin(g(x)) = x? – 25 and g(5) = 0, then g (5):

A:

Q: 15) Show algebraically using composition that f(x)=6x-8-1 and g(x)-( 16) Using the functions in…

A: Step 1: Step 2: Step 3: Step 4:

Q: (cos(2x) – sin(2x)cos(2x)) cos(x) – sin(x) For -dx=-F(x) + C. What is F (x)? 3 A (csc(x) – sec(x))3…

A:

Q: Evaluate the value (a) sin(2) (b) tan (5) (c) sin-¹(√3/2) (d) sin-¹(sin(¹1))

A:

Q: Problem 5 Let B be a nonsingular n x n matrix and let {A1, A2, ..., Amn} be a basis for the vector…

A:

Q: 1 /₁+422da dx 1+ 4x2 15. Evaluate (a) tan-¹(x) + C (d) tan-¹(2x) + C -1 (g) tan-¹(x) + C (j) None of…

A:

Q: D,(6 tan x) 6 sec² x sec² x (c) D,(In |6 tan x|) %3D 6 tan x 6 tan x tan x

A: Consider the given function as Dxln6tanx

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: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

A:

Q: . What is F(/3) if C = 0?

A:

Q: (2+k)dr Evaluate 1– sec (x+a) 1- sec

A: ∫2+k1-secx+adxTake the constant out=2+k·∫11-secx+adx Now,    ∫11-secx+adxLet…

Q: A function f is even if f(x) = f(-x) and odd if f(x) = -f(-x). For example, f is even if f(x) = x2…

A:

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

A:

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: Sketch a graph of the function f(x) = 5 cos| 6+ 3 -87 -71 -6 -SA -47 -3T 27 -T 1 2 3n 47 57 6n 7n…

A: Given: The function

Q: -tan (m + 1)(x) + C tan I + m um + ( x ) (x + ₁)² I m+3 1 с

A: Using substitution then integrating we get correct answer as (C)

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.