1. Let f(x)=x-4x+6x³- - - 5a2+3 1. If you think carefully about your process, the answers to parts (b) and (c) should not be very difficult to determine once you have found the answer to part (a). dy (e) Find T3(x) for f(x) based at b= 1. You do not need to expand your answer. Note: This gives a method for writing a polynomial in powers of (x-1) instead of powers of x. It is sometimes useful if you are interested in the values of the polynomial near = 1. Another technique would be to substitute u = ru+1, multiply out the polynomial, collect together powers of u and then substitute back u=x-1. Using Taylor polynomials is a bit easier. 1 or

Q: y² = 2x = x² 1- y² = (x - 1)² x = 1+√1-y²

A: (a-b)2 = a2 - 2 a b +b2

Q: 4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a)…

A: The given graph of r(x) has zeros at point a , -b and  -c . For the zeros of r(x) , put  r(x)=0 .…

Q: Given f (x) = 6x-2 and g(x)= x² – 3x – 4 , find (f ° g)(x).

A: The given function is fx=6x-2  and  gx=x2-3x-4

Q: If h ( x ) = 3 x 2 − 2 x, then find h (5).

A: Let there is a function fx to find the value fa we need to substitute x=a in the expression.…

Q: Find f(g(x)). 5. f(x) = g(x)=x²-4 x+1 5 7. f(x) = {/ g(x) = √6-x

A:

Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

Q: Consider the functions, h(x) = 3x – 7 and k(x) = . b. Find h(k(x)) X+7 | a. Find h(k(- 2)) c. Find…

A:

Q: 6.Given f(x)= 3x – 2 and g(x)= x2 – 5x, find f(-1)+g(2)

A: The given functions are: fx=3x-2 and gx=x2-5x To find f-1 replace x with -1 in fx=3x-2 and similarly…

Q: i(x) = x² + 3x - 1 2 x4

A:

Q: if f(x)+g(x)= 3x +2 and g(x) = x - 1 then f(x)= %3D а. 2х+3 O b. 3x+2 О с. 3х-2 O d. x+4

A: Given,f(x)+g(x)=3x+2g(x)=x-1f(x)=?

Q: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

Q: For f(x)-2x?+5х +7, fin f (a +h) – f(a) if h ±0. h

A: Given that:fx=2x2+5x+7To find:fa+h-fah

Q: Given that g(x) = 3x-1/x+2 and h(x) = 7x+1/5x-1 a. Evaluate g(3). b. Show that hg(3) = 61/35

A: We evaluate the following function

Q: 4. Find the domain and range of each of the following functions (a) f(x) = 5x – 3 (b) g(t) = y4 – 7t…

A:

Q: 8. FIND f(4) (x) OF f(x) = 3x7 + 4x6 + 8x³ – 2x + 1

A:

Q: 5. Given f(x) =-x+ 3 and g(x) = 2x2 – 5, find the value of f (0) + g(1).

A:

Q: Solve the following differential equation: (3x + 2y + 3)dx + (2x + 4y +1)dy = 0

A:

Q: 1. Find the natural domain f(x) = 3 √2x+1

A:

Q: What is the particular solution for r(x) = 6xe³ª?

A: We have to tell the particular solution for  r(x) = 6xe3x

Q: r {(2) = In(V32" + 5x° + + 6), find f'(r). Use exact values. If

A: Given function is fx=ln3x6+5x3+67      =ln3x6+5x3+617=17ln3x6+5x3+6

Q: Find f(x + Ax) by substituting x + Ax in place of x in f(x) = 9x² - 5x. f(x + Ax) = 9( x+ Ax D² - 5(…

A: To find the f(x+∆x)

Q: Let k(x) 3x – 7 and m(x) = 3x + 1. Find the indicated value. m(x) · k(x) = Complete work must be…

A:

Q: 2 Let s(x) = x ² − 8x + 4 and t(x) = - 2x - 4. Part A: Find s(x) + t(x). Part B: Find s(x) - t(x).

A:

Q: please solve a b

A: Sure, The system depicted in the image consists of a small body orbiting a much larger stationary…

Q: The diagram 4 shows the straight line RST that intersects with the x-axis. The equation of the…

A:

Q: If f(x) = 2x - 4, find f-¹(x). OX-4 2 O-2x+4 O X+4 2 O 4-x 2

A: The inverse of a function f is a function that undoes the operation of f.