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

Q: Let F(z) = f(cos(x)) · sin (금) and G(x) = f(sin(x)) · cos : (주) and suppose that f(0) = 5, f(1) =…

A: We have to find

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: Find f'(x) and f"(x). f'(x) f"(x) = f(x) = (x³ + 7)ex

A:

Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

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

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

Q: Find d can'(x²cosbx) clx

A: To find:- Derivative of tan-1(x2 cos(x))

Q: If Va? – 25 () then f'(6) = f(x) = x cosh

A: Given:

Q: 7. (a) cosh?1 (b) 2 sinh² 20

A:

Q: 3. If f(x) = sinx ex find f'(0).

A: fx=sinxex

Q: Find the derivative. dx sin tdt

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

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

A:

Q: a.) f(x) = sec(e") b.) g(x) = tan¯'(x)+3* +x!5 %3D _1.5

A:

Q: Let f(x) = tan(sec x). What is the slope of the tangent line to at the point X = 0? None of these 00

A:

Q: For the function y (ƒ−¹) '(11) = - ƒ(x) = x² − x − 5, x ≥ 0.5, find - - df dy 1 y=11

A: As per the company guildlines we can solve one question. Please understand.

Q: Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No…

A:

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: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Step 1:

Q: Which of these formulas is appropriate for estimating f'(xx) for the given values of the function at…

A:

Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: If f(x)=sin(sin x) then f'(0) is .. Jika f(x)=sin(sin x) maka f'(0) adalah ... 1. O -1 2. O 1 3. O 0…

A:

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

A: Use product rule:-

Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

A:

Q: 33. (1 + r)' dr

A:

Q: 2. If If ƒ(x) = , find ƒ '(0). et

A: 2) The fx isfx=xex

Q: 3) For the function f(x)=2* the two-point formula to approximate the first derivative of fat xis…

A: Solution

Q: 9. For each of the following functions: a)Find an equation of the tangent line to the curve at the…

A: When tangent line horizontal then slope equal to zero

Q: sin'(-x) = - SI

A:

Q: 4. The range of the function f(r) = sin='(x) is i) [0, z] ii) 2' 2 iii) iv) not listed

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.