22. Rewrite the expression as an algebraic function of x and y: sin(co os'x - tany).

Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

A:

Q: Does the function f(x) = 5x − cos(x) + 4 have a root on [−π, 0]? Justify your answer.

A: Explained below

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

A:

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: dz Find in the function ryz + a’yz = cos (xyz) CoS az

A:

Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

A:

Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

A:

Q: Consider the following. g(x) = V3 cos(2x) + sin(2x) (a) Express the function in terms of sine only.…

A: We know that the following trigonometric identities . sin ( a + b) = sin a cos b + cos a sin b  And…

Q: Differentiate the following function. y = (7 + sin(x))/(7x+cos(x))

A:

Q: 1. Differentiate the following functions: cos (x)+1) sin-(2x), a) y =

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

Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

A:

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

Q: what values of x is f(x) = 2 tan(x + π/6) discontinuous?

A:

Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Find the function if sin t T+1 1 tan 2x + 1

A:

Q: Obtain graphically an approximately value of the root of x = sin x + Tt /2

A:

Q: Find f'(x) given f(x) = cos*(3x). %3D

A:

Q: 3. Explain graphically: cos x dx = 0.

A:

Q: calculate L4 for f(x)=76 cos(x/2) over [2pi/4, 2pi/2]

A:

Q: Q2:- Find the domain of the following functions tanx a) f(x) = %3D sinx-1

A: Domain is value of x for which given function is defined.

Q: 1 For cos2(xy) = , evaluate y' when x = 1.

A: The given equation is cos2xy=14. Calculate the first differentiation y' of the given equation at…

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

Q: 2 = using the relation r= VT show that sin x %3D EX II

A:

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

A:

Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

A:

Q: For cos2(xy) = L. For cos2(xy) =-, evaluate y' when x = 1. 4 3

A:

Q: Show that (Aetkx + Be-ikx)and (C cos kx + D sin kx) are equivalent ways of writing the same function…

A: eix  = cos(x) + i sin(x) e-ix = cos(x) - i sin(x)

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

A:

Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 9. Find f(35) (x) for f(x) = cos (2x)T = COS

A:

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

A:

Q: Evaluate in x cos x dx. .3 I COS" T

A:

Q: Let x = 0.46 and y = 4.74. Determine the value of C when you ev |tan-(2x)dx.(Use 2 decimal digit)

A:

Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: .Write the first two non-zero terms for f (x) = cos(x) about x 2

A:

Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

A:

Q: Let f(x) = cx + In(cos(x)). For what value of c is f' = 4? %3D 4 C =

A:

Q: Obtain the der a) cos(xy)=2y, find y'

A:

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(" = 5? 4

A: Differentiate the given function w.r.t. x.…

Q: Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

A: Given: fx=sinxcos3xf'x=cos4x-2sinxsin3x To find: f''π3=?f'''π3=? Formulas used:…

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

A:

Q: Verify whether the function u=e^(x^2-y^2 ) cos⁡2xy is harmonic or not.

A: A function u=fx,y is said to be harmonic if ∂2u∂x2+∂2u∂y2=0 Now, we have u=ex2-y2cos2xy We will use…

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

A:

Q: If f(x)=e^2x cos(3x), then f’(0) = ?

A: Derivative Question

Q: Find for the following function. sin () + re- cos (2*) = 3y-6z + 8 and

A:

Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

A:

Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…