expressions in terms of exponen - In(coshx + sinhx) + In(cosh 2- cosh5x + sinh5x

Q: True or false If cosh x = then sinh x=

A: We have cheek the statement

Q: If tanx=sinha prove that a=ln(secx+tanx

A:

Q: tan (x) sec²(x) dr. sin²(x)

A: Given  ∫tan3xsec2xsin2xdx using the identities  tanx=sinxcosxsecx=1cosx integral can be written as…

Q: Numerator of X2 over denominator of (x-1)2(x+1)=

A: GivenNumerator of x2 over denominator of(x-1)2(x+1)

Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 01

A:

Q: Derive/prove: sin2x=2sinxcosx

A:

Q: ∫〖sin〗^3 xdx

A: Consider the indefinite integral ∫sin3x dx. To solve this integral first rewrite the integrand using…

Q: 3 lim 2 x2.tan=.sin- X-00

A: We have to evaluate limx→−∞x2⋅tan2x⋅sin3x It can be written as…

Q: sin^4x - cos^4x/sin^2x - cosx =1. prove the identity.

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Q: sin40 Prove 8cos 0 – 4cos0, show preliminaries to perform sino

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Q: lim (3x + 1) sin(2x) 4x2

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Q: tion to the differe where k is

A:

Q: = cosx (sinx). 2. Find the Fourier series on -≤x≤π for f(x) =

A: Given the function fx=cosxsin2x, -π≤x≤π

Q: 1. sin (-x)(sin(-x) + 1)

A: Given; Sin(-x)[Sin(-x)+1].

Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: sin x 1+ cosx 1+ cosx + sin x 2cscx 2secx 01

A:

Q: 3tan3x=tanx in the interval [0,2pi

A: Given,3 tan3x = tan x3 tan3x - tan x = 0tan x (3 tan2x -1)=0tan x =0            ;     3 tan2x-1 =0…

Q: sin(2n) 1+/n In %3D

A: Write in product of two sequences

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: A 70 (x) -(5n4x) 140° (sin

A: The given data is: [12x-18sin4x]40∘70∘  To find the value of the given data.

Q: sin20 6. ) lim tan³0 0- 4

A: Given: limθ→π4sin2θtan3θ

Q: tane 12. lim 80 sin20

A: First of all substitute the value of the limit that is 0 in place of θ in the function.…

Q: sin²(x) 2. If f(x) = - x show that the single-point method for solving f (x) = 0 will 2 converge.

A: In a single-point method, x=ϕ(x) will converge if ϕ'(x)<1. Given, f(x)=sin2x2-x To show, that the…

Q: Prove that cosX + sinX ≤ ✓2 using a method of proof by contradiction. If possible please write in…

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Q: Limit as x approaches 0 of Sin(5x)/(2x

A: Limit as x approaches 0 of Sin(5x)/(2x

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 1

A:

Q: sin (-11x) lim x→0 _tan(9x)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ) Write sin(2 sin-(3x)) in terms of x only. (i) 6x/1 – 9x² (ii) 6x (iii) V1 – 9x² - (iv) Not listed

A:

Q: sinx 0 cosx –sinx cosx is non singular for all values of x. 1 lect one:

A:

Q: USing Inverse find Particular Solution of Differen tial ofera tor to 9 -48= Cosh (2X -1) + 3

A: We use following formula while calculating particular solution using inverse differential operator…

Q: prove that cosh^2x-sinh^2x=1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: square root of 2 sin2x-sinx=0

A: Given:

Q: integral sin2 x cos3 x

A:

Q: Sin 2X 2. X 3 tan 2X

A: Equating the first derivative of a function to zero and solving the equation for the variable will…

Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: lim x approches 0 of sin(5x)/7x

A: We have to calculate; A=limx→0sin(5x)7x

Q: 8) lim(-) sinx-cosx 10) lim TU

A:

Q: Verify the identity. (Simplify at each step.) sin3/2 x cos x - sin72 x cos x = cos3 xV sin3 x .…

A: Here we solve the trigonometry equation.

Q: sin 3x 39.lim tan 6t 41. lim 50 sin 21

A: We will use the l'hospital rule to fine the limit of 39.  To fine limit 41. We will use the basic…

Q: lim n sin (- n

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Q: 1. f(x) = cos 2x - Show the solution of the derivative using F'el trigonometric identity that it…

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Q: give 3 basic derivatives examples of sum rule with solution Avoid using: cosx, sinx, tanx, logx.…

A: 1fx=x2−2xDifferentiate w.r.t "x"f'x=ddxx2−2xf'x=2x−2

Q: Find all values of x in the interval [0,2pi) Tanxcsc^2x-2tanx=0

A:

Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…

Q: Applying mean value theorem to fx=sinx, one can show that sinx( less than or equal) x for each x…

A: this is true.

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

Q: imit x to infinity sin3x/2x

A:

Q: التاريخ Sinho SechG)

A: Answer and explanation is given below...

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.