(6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

A:

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

A:

Q: 8. Find the principal value of Arc tanh(1 + j2)

A:

Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

A:

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

A:

Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

A:

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: sinh In(2+2x) dx? x+1

A:

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 (-24 x² – 10x³ -…

A: Given integral is ∫-4-1 -x4 -10x3 -24x2 -4x+4 dx Take  fx = -x4 -10x3 -24x2 -4x+4

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

Q: 2 sin x f(x) = 1+2cos x Pvaluated at x = 1 ran

A: Given: fx=2sinx1+2cosx

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

A:

Q: The area under the entire curve is given by 00 dx. We have 3x-3 dx = lim 3x-3 dx -2 3x lim %3D -2 x…

A: the area under the  entire curve is given by ∫1∞3x3dx

Q: 30. 5e dx 31. Зи du - 1 33. x² dx 35. (x+5)* 37. xp (3 In z + 2)4 39, -dz

A: We will solve the integration.

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: 3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

A: I=∫03sin4xdx Integrating it- I=-cos4x403=-cos124+cos04=1-cos124=0.0054

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

A:

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: Use Property 8 to estimate the value of the integral.

A:

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: 3. Evaluate tan¹x² 1+x dx.

A:

Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

A:

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: Given the integral sin(3x + 5) dx cos(3x + 5)

A:

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

A:

Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x*+20x-126x + 2x +3 dx…

A:

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

A:

Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

A:

Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.