Let g be the function defined by g(x) = x(x + 1). Find g(x + h)...

Let g be the function defined by g(x) = x(x + 1). Find g(x + h) − g(x − h).

Expert Solution

milcah answered 2 years ago

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

Let f be the periodic function defined by f(x) = 1 + x|x|, −1 < x...

Let f be the periodic function defined by f(x) = 1 + x|x|, −1 < x < 1, and f(x) = f(x + 2). Find the Fourier series of f.

Let G be an abelian group. (a) If H = {x ∈ G| |x| is odd},...

Let G be an abelian group. (a) If H = {x ∈ G| |x| is odd}, prove that H is a subgroup of G. (b) If K = {x ∈ G| |x| = 1 or is even}, must K be a subgroup of G? (Give a proof or counterexample.)

Let G and H be groups. Define the direct product G X H = {(x,y) |...

Let G and H be groups. Define the direct product G X H = {(x,y) | x ∈ G and y ∈H } Prove that G X H itself is a group.

Given that h(x) = x.sinx . Find the root of the function h(x) = 1, where...

Given that h(x) = x.sinx . Find the root of the function h(x) = 1, where x is between [0, 2] using substitution method.

Given that h(x)=x+3 and g(x)=sqrt of x-4, find (g+h)(4), if it exists.

1. For the function f(x)=x2−36 evaluate f(x+h). f(x+h)= 2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate...

1. For the function f(x)=x2−36 evaluate f(x+h). f(x+h)= 2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate the following: a. (fg)(3)= b. (f/g) (2)= c. (f/g) (0)= d.(fh)(-1)= 3. Let f(x)=2x-1, g(x)=x-3, and h(x) =2x^2-7x+3. write a formula for each of the following functions and then simplify a. (fh) (x)= b. (h/f) (x)= c. (h/g) (x)= 4.Let f(x)=5−x and g(x)=x^3+3 find: a. (f∘g)(0)= b.(g∘f)(0)= c. (f∘g)(x)= d. (g∘f)(x)= 5. Let f(x)=x^2+5x and g(x)=4x+5 find: a. (f∘g)(x)= b. (g∘f)(x)= c. (f∘g)(0)= d....

Let F(x) = log5x and H(x) = x . Find the value of F(H(25)). Write the...

Let F(x) = log5x and H(x) = x . Find the value of F(H(25)). Write the equation of a circle whose center is located at (-2, -5) with a radius of 11 inches. Given a triangle with Angle A = 45 degrees, Angle B = 60 degrees and side a = 10 inches. Find the length of side b. (Leave answer in radical form.) Find the distance between a set of points whose coordinates are A(-7, 8) and B(5, -11)....

Utility function over clothing (C) and greens (G) is defined by the function U(C,G)=C^(1/4)+G^(1/4). Let P(of...

Utility function over clothing (C) and greens (G) is defined by the function U(C,G)=C^(1/4)+G^(1/4). Let P(of C) and P(of G) denote the prices of cherries and grapes respectively. W is income that is available to consumer to spend on those two goods. (a) Write down the customer's utility maximization problem. (b) set up the langrangian and solve for the first order condition. (c) Solve for the consumer's demand functions for clothing and greens. Please Explain.

6. (a) let f : R → R be a function defined by f(x) = x...

6. (a) let f : R → R be a function defined by f(x) = x + 4 if x ≤ 1 ax + b if 1 < x ≤ 3 3x x 8 if x > 3 Find the values of a and b that makes f(x) continuous on R. [10 marks] (b) Find the derivative of f(x) = tann 1 1 ∞x 1 + x . [15 marks] (c) Find f 0 (x) using logarithmic differentiation, where f(x)...

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