Let f:[-r, 7]→ R, where f (x) = 2 sin(2x) – 1.

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

A:

Q: Express the function in the form  f ° g

A: It is the composition of two functions, they are

Q: What is the range of the function f(x) = 2 cos x + 1? [0,3] O[-2,2] O[-2, 1] O[-3,0] O[-1,3]

A: f(x)=2cosx+1

Q: Test the sets of functions for linear in­dependence in F For those that are linearly dependent,…

A: Given: A set of functions is 1 , sin2x , cos2x. To Find: If the given set of functions are linearly…

Q: Q2. Prove that sec2(tan-x) = 1+ x?

A:

Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

A:

Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: Compute fFdr, where F(x, y) = (5+27x², 2xy) and C is a line segment from (0, 0) to (1,2). (Use…

A:

Q: Let f : R → R be a twice differentiable function such that f" + f = 0. Prove there exist constants…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: What is the range of the function f(x) = 23 sin 4x+1 ? A B [0, ∞) D [4,16] C) [1,4] [2,00)

A: Range is the set of y values corresponding to x values of domain.

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

A:

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

A:

Q: Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n…

A:

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

A:

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

A:

Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

A:

Q: The principal part for a) 5 b) 2 for xo of f(x) = 2 + 5+ sinx with respect to ↓

A: Given that .Let .We need to find the principal part of f(x) with respect to g(x) as x→0.We will use…

Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: 1-x The equation of the tangent line for y = at (- 2, – 3) is 1+X

A: AS PER GUIDELINES I CAN ATTEMPT ONLY FIRST QUESTION

Q: The domain of f(r) =tan(x) is Select one: a. 2 2 O b. IR - + nn} O c. IR O d. R {nt}

A:

Q: Show that sin x < x for all x ∈ (0, 2π).

A:

Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

A:

Q: What is the domain of f(x)=Dsin1(IIn(x)l)? %3D Select one: O (0,e] O (0,00)

A: Given, fx =sin-1lnx  We have to find the domain of  fx =sin-1lnx

Q: How many people need to attend a party for there to be a > 80% probability that at least two of them…

A: Given information: The probability that at least two of the people share the same birthday is 0.8.

Q: 04 Let f(x) be a contineous function such that Ler - 5/W)dx = = 4 and =9, then a) 81 b) 101

A: Use definite integration property