In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

Q: 20. Evaluate.d(x³ sinh(Inx)) O a. 2x3 − x O b. 2x² O C. 4x²-x O d. 2x2 − x

A:

Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

A:

Q: If y- In(3 sinh( 3lnx)), then xy'= Select one: O3 coth( 3 Inx) O 3 /sinh( 3 Inx) O 9 coth( 3 Inx) O…

A: Use the Chain-Rule of differentiation to differentiate the function y.

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: Find the indefinite integral. Solution in handwritten a. S sin x -dx cos²x

A:

Q: Solve the integral. sin x dx 10. cos2 x + cos x – 2

A:

Q: In( cosh(3x)+sinh(3x) )= Select one: O- 3x 01 O None O 3x O3 sinh(3 x +

A:

Q: If xy In(3 sinh( 3x)), then x2y'= %3D Select one: Ox coth( 3x ) - In( 3 sinh(3x)) 09x coth( 3x ) - 3…

A:

Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

A:

Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: %3D In( cosh(9x) + sinh(9x)) + In( cosh(9x)- sinh(9x)) = Select one: O None 0 9 O zero O9 cosh(9 x)…

A:

Q: Evaluate the integrals sin2.x -dp- J(5 + cos2.x) e) 3

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

Q: Solve the integral. sin x dx 10. cos2 x + cOs x – 2

A: Given: ∫sinxcos2x+cosx-2 Let u=cosx, thendudx=-sinx and dx=-1sinxdu.…

Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

A:

Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

A:

Q: Find the indefinite integral. ∫cos5 x sin x dx

A: ∫cos5x sinx dx Put, cosx=t⇒-sinx=dtdx⇒-sinx dx=dt⇒sinx dx=-dt

Q: Find the indefinite integral ∫cos 2x cos 6x dx

A: Given integration as I=∫cos 2x cos 6x dx Since  2cos 2x cos 6x=cos 6x+2x+cos 6x-2x…

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x + 2 = 0. b. Express tanh x in terms of e*…

A:

Q: Find the indefinite integral. | x cos 9x² dx

A: Given : ∫xcos(9πx2)dx

Q: In( cosh(8x) - sinh(8x)) - In( cosh(9x) + sinh(9x) ) = Select one: O zero O 17x O None Ox O 8X O- 17…

A:

Q: 12 cos6x. sin³ xdxCalculate "/2 3 the integral

A: It is integral problem.

Q: 22. Evaluate dr. x2 – 8x – 9 - a. cosh-1 -4 b. 4 cosh-1* – 4 +C C. sinh-1 – 4 5 +C d. 4 sinh-1 - 4…

A:

Q: The value of the integral (x–1)* sin (x 1) (x-1) +cos (x-1) is

A:

Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

A:

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

A:

Q: In( cosh(3x)+sinh(3x) )= Select one: O 3 sinh(3 x )+ 3 cosh(3 x) O- 3x 01 zero None O 3x

A: Formula to be used sinh x = [ex– e-x]2cosh x = [ex+ e-x]2

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: sinh(Inx)= Select one: x² –1 2x O None O 2x x² +1 2x O zero

A: We know that sinh(x)=ex-e-x2. So,           sinh(ln(x))=eln(x)-e-ln(x)2…

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

A:

Q: sinh (1+Inx)= Select one: ex-1 2xe O Zero e Inx 2 O None e?x² +1 2xe x² +1 O 1+ 2x

A:

Q: If e/½i =sin2 then z = - 2i In(sin2) + 4k TI 2i In(sin2) + 4k T - 2i In(sin2) – 4kT -2 In(sin2) + 4k…

A: We will find the solution

Q: cos(9x) -dx COS J 1+ sin²(9x)

A:

Q: 1. Show that x = sin (Int) is a solution of t2: (5) 0 = x +1+.

A:

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

A:

Q: 211 3- sin nx dx [1-cos2nx]dx 1t, where n integers.

A:

Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Find the indefinite integral. sinh(2 – 9x) dx

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.