a. Find the root mean square value of tanh x, for 0 < x< 2.

Q: Compute the following: e) dx (2019 + seC x tan x (b)() dr

A: a) The given integral is evaluated as follows.

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

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

Q: sinh x dx 1+ cosh x

A:

Q: 6. Use the Successive Approximation method to find correct to four significant figures a real root…

A:

Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: FInd the intervals in which the function f(x) =sin(logex) +cos(logex) is decreasing

A: Given function is, f(x)=sin(logex)+cos(logex)

Q: For x >0, tanh(Inx)+ dx x2 - (tan-(x)) 1 + > = x? .2 Select one: O True O False

A:

Q: Find the mean value of sin 2x over the interval (0,x)

A: Solution is given below:

Q: 1 Find the mean value over the interval [0,2n]. 4+cosx

A:

Q: Using e and e expansions, find sinh x.

A:

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: Evaluate the followingintegrals.∫x3√(2x+1)dx

A: Given integral is ∫x32x+1dx. Consider u=2x+1. Then du=12x+1dxdx=2x+1dudx=udu

Q: Use a graphing calculator to evaluate the integral 2 e dx.

A:

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Find cosh a In(sinh r)dr.

A:

Q: Find the length of the graph of f(x) = In(4 sec(x)) for 0 < x <. %3D a) O1/4 In(3) b) 03/4 In(3) c)…

A:

Q: evaluate the following intergertal     (e−x + 2x)2 dx

A: Given integral is By using the identity (a+b)^2=a^2+b^2+2ab, we get

Q: 1 dx x(In x)*

A:

Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

A:

Q: Find the root of the function ((x) =sin x -e in the interval (0,1) using the formula g(x) =aresin…

A:

Q: 2. Find all values of 0 in the interval [0°, 360°) that have the given function value tan 0 = -V3.

A:

Q: Evaluate the integral two log e base 10, over x times dx, from x = 1 to 10.

A:

Q: Find a harmonic function o on the upper half-plane that takes values ø(x) = 0 for |a| > 1 and $(x) :…

A: Sol

Q: Use the Intermediate Value Theorem to show that  there is a root of the given equation in the…

A: Given : ln(x) = x - sqrt(x) , (2,3)

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

A:

Q: d41 -cosh(x) at x : O is dx41

A: cosh (x)

Q: Determine all the critical points for the following:- f(x) = sin?x - cos x On the interval (0,2n).…

A: A point c is said to be critical point of a function f(x) if f'(c)=0 or does not exist. Given…

Q: ) Evaluate the following integrate S tan-1 xdx

A:

Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: Use the definition in terms of exponential functions to prove the following 1.tanh(In x) %3D x2+1

A:

Q: cosh(2x) = cosh?(x) + sinh² (x).

A:

Q: Q6) Calculate the mean value of y= 24 sin5 0 cos 0 from 0 = 0 to 0= J\6

A: Mean value is evaluated.

Q: Evaluate the following derivative. ar (x In (x10)) a (x In (x'0)) = D dx

A: Given: y=xlnx10 we know that ddxu.v=vdudx+udvdx                                    ..1

Q: Find the extreme values for the function f(x) = x + sin x on the interval [0, 27).

A: This function is unbounded below and unbounded above, Therefore the function has no global extreme…

Q: On what interval is the formula (tanh x) 1 dx 1- valid?

A: Given: ddxtanh-1x=11-x2

Q: el+x By using the definition In(1+x) = 1 -dt, show that for a certain range of values of r,…

A:

Q: S 3* e*dx

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

A: Here fx=x1-x2 The interval is 0,1 and n=5. Hence the interval is divided into 5 equal parts.…

Q: Evaluate the definite integral. e2 - x dx

A: The given integral is as follows. Let u=2-x. Then, du=-dx. The Lower limit will be u=2-2=0 and the…

Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

A:

Q: (a) Use the definition of L{-} to determine L{te="}

A: As per the rule one question is solved at a time so i am solving (a). Consider the given Laplace…

Q: (a) Define the following hyperbolic functions directly in terms of the exponential function (i)…

A:

Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

Q: Evaluate the following integral π/4 x tan(x²) dx

A: Let us assume u=x2So, du=2xdxor, du2=xdx

Q: If df between= 3, and df within=60, if alpha is set at 0.5, then f crit =

A: Given:Degrees of freedom between = df1 = 3Degrees of freedom within = df2 = 60Level of significance…

Q: Find a value of x such that is equal to (a) ln 5 and (b) 1.

A:

Q: S(a – x)°dx

A: We need to integrate given function.

Q: Determine the value of x that satisfy the following equation; sinh-1x = In(3 – x²) – In(x + v3).

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.