..LH.S.-R.H.S. - HW/ Prove that: (1) 1-tanh x=sech'x

Q: nd the hundredth derivative of p (x) = (x + x + x')1°(1 + x²)'' (x³ + x° + x'). Justify your answer.

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Q: He)=(x+2)e f has absolute extreme values on ?

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Q: find Using your results from problem #3 the equation of the tangent line for f(x)... when -20 2-2…

A: We have to find the tangent line equation

Q: r(t) = ( tan(7t), sec(8t), -'(t) =

A: rt=tan(7t),sec(8t),1t2 We have to find r'(t)

Q: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

A:

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: 4-x 2. s] Let f(x) = . It was computed thatf'(x) = (x² +4)z" Find where the function is increasing…

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Q: Find the derivative. dx sin tdt

A: We have to find the given derivative ddx∫0x5sin t dt.

Q: 5. f(x)=e* cos x + e* sin x

A: We use Product rule  ddxuv=udvdx+vdvdx

Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

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Q: At any point (x,y) on a particular curve, the tangent line has a slope equal to 1+ sin (x 5) If the…

A: At any point (x,y) on a particular curve, the tangent line has a slope equalto 1+sinx-π2, the curve…

Q: 26 Functions f(a) and g(x) and their first and second derivatives evaluated at z = 1 are listed as…

A:

Q: 9. 10. If f(x)=√ex, the derivative is: √ex a) f'(x) = Vex b) f'(x) = √ex c) f'(x) = 2x Which of the…

A: Calculate the derivative of both problem in the following way:

Q: 3pts) Find the equation of the tangent line to the graph of the function f(x)=x-Vx at the point…

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Q: Which of the following refers to backward - difference formula? Why? You can give your own example…

A: We need to compare with general formula of backward difference.

Q: Complete the statements.

A: Given Our aim is to complete the sentence

Q: b) y= In( see x)

A: Answer and explanation is given below..

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Step 1:

Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: p(t) = 1 √√/t²

A: Here we have to find the anti derivative i,e integration of p(t)Given p(t)=1t23or, p(t)=t-2/3

Q: flx) glx) g'ix) 1 2 4 2 1 8 5 7 3 7 2 7 3.

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Q: C) It is given that f(r) = tan¯*(1 +x). (i) Find f(0) and f '(0), and show that f "(0) =

A: Given Fx=tan-11+xwe find F0,F'0 and prove F''0=-12

Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: b- Find L' by(Gonvolu fion theorm)

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Q: Q3) Find the derivative of y for all functions the following (3) y = tlog3(e(stn t)(In 3)) %3D

A: The derivative of the logarithmic terms can be calculated by first simplifying the logarithm. The…

Q: 25) y= Arctansinh x

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Q: 6. Find y' in each case. Do not simplify your answer. 2 tan x C) y = VI – x² - d) xªy + 5y®x³ = 8.…

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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.