sinh5x S sinh*xcoshx dx is a)True b)False

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: Q3) Ify = in[sec 8 + tan 8) find

A:

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: s nip

A: Given z=tanα2

Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: కషిద్టి చవీ / tangent s lope rosin (20) when Jot 5 2) 653 3. not of the above

A:

Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

A:

Q: If Y=tanx prove that %3D2

A:

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: 7. Integrate. S tan50 sec³0d0

A:

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

A:

Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

Q: Show that O tanh(In x) = (cosh x + sinh x)" = cosh nx +sinh nx

A:

Q: Integrate sin" uelor (cosu) . Where n=540

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

A:

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

A:

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: 5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

A: The complex function is of the form z=x+iywhere x is the real part and y is the imaginary part. A…

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

A:

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A:

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: Prove the identity: sinh2x=2sinhxcoshx

A:

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: converges or div rge 2n+ Sinln)

A: The given series is  ∑n=1∞ 12n+sinn We have to check whether the series converges or diverges.

Q: Prove that : 1. Sinhx= In(x+x² +1)

A:

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: Lim メーvo s'in 5À sin 3X

A: Given: limx→0sin5xsin3x

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.