Prove cosh 2 x - sinh 2  x =1

Q: 1. Find the exact length of the curve for r(t) = (√√2t, √√2t, t²), 0≤t≤1 (Note: The variable t is…

A:

Q: sinhx dx 1+ coshx ) A 1+ coshx B (1+coshx)? (1+coshx)² D 1+ coshx

A: We have to find

Q: csch-1 x= x = sinh sinh11 X Prove mathematically that the right-hand side is equal to the left-hand…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

Q: L{sinh 6t– cosh t

A: we have to find the value of L{sinh(6t)-cosh(t)}

Q: d 1+ sin² (2)| dz

A:

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Use the addition formulas for sinhx and coshx to prove that tanh(u+v)= tanhu+tanhv/ 1+tanhutanhv

A:

Q: Show that z- sinh z Rcs :* sinh z

A:

Q: show that sinx less than x if 0 less than x less than 2pi

A: Assume that, fx=x-sinx Differentiate f (x) w.r.t. x, f'x=1-cosx=2sin2x2

Q: cosx Show that J-3(x) = -. + sinx)

A:

Q: Find Sor y. Sin X- xp X+1

A:

Q: Verify the identity sinh(x + y) = sinh x cosh y + cosh x sinh y

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.