59. y = tan(4x²), x = /T

Q: Find y′ if y = tanh−1(sinh x2).

A:

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

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

A:

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

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

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

A:

Q: Integrate O sinh 2x dx

A:

Q: Ex Evaluote S 4e sinhx..dx

A:

Q: 2 9) -sinh? -cosh -dz

A:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

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

A:

Q: 17 0 in QII 32. sec0= - mot 15

A: Given:secθ=-1715,  θ in quadrant 2

Q: Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

A:

Q: Solve for Xi 31 In x =D 늦 (Inle t 21n2) %3D

A:

Q: 2 L sinh–t|= 3 6. 9s2 – 4 3 2s2-4 6. s² – 4 - 3s2 – 4

A:

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

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

Q: Find y' if y=In(tanhx) +cosh¬1(coth2x)

A:

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: Find y' if y= In(tanhx) +cosh-(coth2x) Select one: O y' = cothx- 2csch2x 1 O y = -2csch2x sinh x…

A: The differential of products of trigonometric functions can be calculated using the product rule.…

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

A:

Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

A:

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: Find the indefinite integral ∫sinh 6x dx

A:

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

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 , if y = x sinh x - cosh x %3D dx

A:

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

A: To find:∫sinh4-5xdx

Q: 3 sinº x dx 4 Show that

A:

Q: Find the indefinite integral. S sinh (1 – 2x) dx

A:

Q: 0 ex [ 224²1 ex + 1 J-In 2 dx

A:

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: S tanʼx dx

A: Answer is given in next step.

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: Use differentials to approximate the quantity   √99.7

A:

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

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: 4. If y = x cos x determine the 5th derivative. [y6) = (60x – x³) sin x+ (15x? – 60) cos x] |

A:

Q: 3. Jメニ

A: We can find the antiderivative as below

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

A:

Q: Use differentials to approximate tan (43°). Round to 4 decimals.

A: Approximate to tan(43°) using the differentials ,

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.