(COMPOSITION OF FUNCTION) 1.) Let: f(x)= 3x+4 Find (fo f)(x) 2-4) Let: f(x)= 2x+1 and g(x)=x+3 A. Find (f° g)(x) B. Find (g o f)(x) C. Find (g o g)(x) 5.) Let: f(x)=3x+2 and g(x)= x+5 Find (g o f)(x)

Q: Given f(x, y, 2) = 4 sin(x + y), find f,(0, . -3), F,(0, -3), and f-(0, -3). 4 -3 4 40. -) - 4 II II

A: Answer is 0  Explanation is given below..

Q: 6.4.1 Example Let the function f be equal to (Ayk)²; therefore, equation (6.52) becomes Yk = kak +…

A: In the given question we have to explain the equation ∆xk = 0and yk = ck+c2…

Q: . 3. Given the functions f(x)=3* and g(x)=cos x (a) Determine the domain and range of y=f(g(x)) (b)…

A: Here given that the functions are                                 f(x)=3x and g(x)=cosx We have to…

Q: a. Show that Y is a biased estimator of 0 and con b. Find the MSE of Y. c. Find a function of Y that…

A:

Q: 3 27 -x+39 2 For the function f(x)= - - 4 3 G) Determine the coordinates of the turning noints

A:

Q: If f(x) =x* +;x-x+ 2, then f is concave up on %3D A) (0, co) only. B) (-3,0) only. C) (-00,-3) only.…

A:

Q: 2. Find the function that satisfies these conditions: 7 (t) = (e', sin t, sec² t); 7 (0) = (2, 2, 2)

A: Ffff

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y),…

A:

Q: 2. Graph the function f(x) = cos(2x) +1. %3D

A: y=cos2x+1 to graph the function, we need a few points x y=cos2x+1 -2π 2 -7π4 1 -3π2 0…

Q: Find f(x).

A: Given,

Q: Find a harmonic conjugate of the function u(x, y) = arctan(x/y)− 6

A: Solution :-

Q: 5:) f (x) = a)? find the 3 finst f g and h uch that (fo gon) (x)

A:

Q: (a) Find a function f(x) satisfying the conditions f' (x) = cos(x), f(0) = -2, f' (0) = 6, f"(0) =…

A:

Q: x2 -9 + т, х# 3 Let f(x) = x-3 тx + 3k, x = 3 Is cont. at x = 3, find the value m&k if f(-1) = 8.…

A: Givenf(x)=x2-9x-3+m, x≠3           mx+3k ,    x=3To check f is continuous at x=3.

Q: 2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation,…

A:

Q: [3] Let f(x) = –x³. find p2, P3, and p4. Cos x and po = -1, pi = 0. Use the Secant method to

A:

Q: 10. Find the period of the function: g (x) = 3 tan (6z + 42) %3D 6. 42 3, kl3

A:

Q: Q1) Find g'(fx)) if you know that g(x) = 3cos(x- 5), (x) = cot(x²) at x = 2

A:

Q: (a) State the implicit function theorem in two dimensions. (b) Verify that the equation f(2, 3) = 2²…

A:

Q: (1+x² +C B [2x (1+x) dx-A)- 11 10 11 f(x)=x+cosx, xe [0,7), then the function has an inflection…

A: from graph  stationary point: point of function is a point where the derivative is equal to zero .…

Q: (a) Find a function f(x) satisfying the conditions f"(x) = -27 cos(-3x), f(0) = 7, f'(0) = 4, f"(0)…

A:

Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: Given a function f(x,y,z) = (x+9) ln (2y - 3) sin (5z). Find the range of the function. a.[ -1, 1 ]…

A: We know,  Range of sinx = [-1,1] for all real x. Range of ln(x)=-∞,∞ for all real x Range of a…

Q: Let g(x) = (arccos x?)5. Then g'(x) = %3D A) -10*(arccos x)4 V1-x x(arccos x?) V1-x B) -10 C) -10…

A: Solution: Given g(x)=cos-1x25 To find g'(x)

Q: 2-x Q.1 Write the function f(x)= as the sum of cosx+3x an even and odd functions.

A:

Q: [4] Let f(x) = -p³ Position to find p2, P3, and p4. cos x and po = -1, pi = 0. Use the Method of…

A:

Q: (a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

A: Topic = Derivative

Q: 11. Determine if the function is even, odd, or neither. a. f(x) = 6x* + 7|x| b. g(x) = 6x* + 7x c.…

A: Given:  a.f(x)=6x4+7xb.g(x)=6x4+7xc.h(x)=6x3+7x

Q: Find f. f '(t) = 6 cos t + sect, -x/2 <t< x/2, f(x/3) = 5 %3D

A:

Q: 19. What is the number of zeros of the function f(x) = e* – sin(x)? O a) It has no zeros. O b) It…

A: Graph the given function as shown below:

Q: sec a f(x) = is discontinuous at the point Select one: O a. r = 0 O b. x = T O c. r = ,n is even O…

A: Answer is  d) We apply property of contunity

Q: f:[0,1] -> [0,1] such that f(x)=x^2 has two fixed points. Is this true?

A: Given that f:[0,1] to [0,1].

Q: 3. (a) Determine whether the function y=1-cosx is even, odd or neither. (b)Find antiderivative of 3…

A: Consider the given function as y=1-cosx. Check the function is odd or even as follows. let…

Q: 7. Let f(&x) = tan-(y/x). Find and simplify fg and f Then find and simplify ffe, and fy-

A: Topic-derrivative

Q: 1 find the domain and range of f(x) 2 - cos3x

A:

Q: The domain and the range of z=cos-¹(x²-y-3) are represented respectively by A. None of the choices…

A: We have to find the domain and range of z = cos-1(x2-y-3).

Q: (a) Two function f(x) and g(x) are called orthogonal in the interval [ab] if they satisfy the…

A:

Q: If f(x) = tan-'(2x) , then f'(x) = %3| (A) H 1+4x2 2 (B) 1+x2 (C) 구1 2 1+4x2 (D) I-Aa2 V1-4x2 (E)…

A:

Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

A:

Q: Regarding the function f(x) = cos(2æ) +7, answer T if the statement is true as described and F if it…

A: Trigonometric functions are elementary functions, the argument of which is an angle. Trigonometric…

Q: dx = In[F(x)]+C.What is F(3) if C= 0? For %3D (x+x³) (x Tan-x+ 1) A B -1 + 3 D -15 -15

A: Please see the below picture for detailed solution.

Q: 1. Does the function V(x,y) e-3xcos(2y) harmonic. %3D

A:

Q: 8. Consider the functions f : (4, 0) → R where f(x) = sin x and g : (-12,3) → R where g(x) = |x +…

A: Solution

Q: 6. Give the slope of the line that passes through the points P and Q on the graph of f(x) = = COSx…

A: The given function is,

Q: 9. The functionf is such that f(x) = 3 – 4 cosx, for 0 <x<T, wherek is a %3D (i) In the case where k…

A: As per our guidelines we are supposed to answer only one question.* *Kindly repost other question as…

Q: Find the absolute maximum and minimum values of the function f(x) = cos²x-3sinx on the interval…

A:

Q: B 1. f(x)= (-2x, xS-2 a. (-o, -1), [-1, ∞) -x² -1,x>-2 2. f(x)=- 2x-4 b. (-0, 2), [2, ) 3. f(x)=…

A: GivenMatch each function in column A with its corresponding interval in column B. Write the letter…

Q: dx = In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-x+1) (A +- B V3 + 3 -1 D -1s -is -is

A:

Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: 1. Consider the function f(x, y) y exly for x > 0 and y > 0. Find the value(s) of the constants a…

A: Given: fx,y=yaebx2y for x&gt;0 and y&gt;0 and ∂2f∂x2+2x∂f∂x=∂f∂y Now, ∂f∂x means partial derivative…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.