If y = tanh"(k/x) and x (1 - 144x) y'=A Then A= .

Q: If h(2) = 7 and h'(2) = -6, find 'h(x)' 미 dx X x = 2.

A: The derivative of the two functions in division form is given by the quotient rule.

Q: IX. Find y' if 1. (5 pts.) y = 2 In (cos (Tx)) 2. (6 pts.) y = csc² (Arcsec (Va) + e-)

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Q: 1 Y(s) 4 5s2 S

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Q: 5). § sech x tanh-x dx

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Q: if y= (1+e^x)X^3 then find y`

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Q: 1 ["Co 0 Approximate e cos x dx using 0 P₂(x) dx OA. 1.75 OB. 1.25 O c. 1.125 O D. 1.5

A: Sol:- First find P2xA Maclaurin series is given byf(x)=∑k=0∞f(k)(a)k!xkIn our case,…

Q: g(t)=−4t^7e^t−2sintcost whats g'

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Q: sec?xsec'y dx dy .2

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Q: Calculate y'. y = ln(x ln x)

A: Given: y=lnxlnx The objective is to calculate its derivative. Chain Rule for Differentiation: ddxf…

Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

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Q: if y= 1/2x^3 then find y`(0.50)

A: We find y' or first derivative of y using power rule. d/dx(x^n)= n*x^(n-1)

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: xy' +by = 0

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Q: Find y' for the following y= x^lnx

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Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

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Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

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Q: Find the derivative of h(x) = O O a.) h'(x)= b.) c.) d.) ܝܕܝ h'(x) = h'(x) = h'(x)= 2 Waiting for…

A: Solve for the derivative

Q: Differentiate. y = 1 — х* y' =

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Q: d 61. tanh(e*) = e* sech²(e*) dx

A: It is given that, ddxtanhex=exsech2ex.

Q: A company finds that the revenue R generated by spending x dollars on advertising is given by R =…

A: To find: The value of dRdx at x=1500. Given: The revenue generated function is R=1000+80x-0.02x2.…

Q: If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)

A: Answer: Given that, P(A or B) = 0.801 P(B') = 0.33 P(A and B) = 0.20

Q: Calculate y', y" and y" for y = . [Hint: y= r-le", product rule, several times.] use

A: Topic  - differentiation by parts

Q: f y^x = e^1/x, then y' is equal to what

A: we have to solve the problem

Q: 6. (a) e' sinht (b) 3e2 cosh 4t

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Q: dy y'= 3r?y = dx Up to y''only. For 0sxs2; y(0) = -1;h=0.1

A: Given y'=3x2y2     (1) Differentiating with respect to x, we get y''=6xy2+6x2yy' from (1)…

Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

A:

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.