a) let f(x)= x^3-9x verify that on [-3,3] meets the requirements of rolle's therom, please show...

a) let f(x)= x^3-9x verify that on [-3,3] meets the requirements of rolle's therom, please show how, then all c's that rolle's guarantees.

b) find the linear approximation of f(x)=cos(x)g at x=pi/4 then use it to approximate cos(pi/3)

Expert Solution

milcah answered 2 years ago

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....

Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f is injective, but not surjective. (b) Suppose g : R\{−1} → R\{a} is a function such that g(x) = x−1, where a ∈ R. Determine x+1 a, show that g is bijective and determine its inverse function.

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and such that f(a)=f(b). Then there exists at least one point c on (a,b) such that f'(c)=0." Rolle's Theorem requires three conditions be satisified. (a) What are these three conditions? (b) Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow, i.e., there is no point c in (a,b) such that f'(c)=0. Each...

Given f(x)=2x3-7x2+9x-3, use the remainder theorem to find f(-1)

(abstract algebra) Let F be a field. Suppose f(x), g(x), h(x) ∈ F[x]. Show that the...

(abstract algebra) Let F be a field. Suppose f(x), g(x), h(x) ∈ F[x]. Show that the following properties hold: (a) If g(x)|f(x) and h(x)|g(x), then h(x)|f(x). (b) If g(x)|f(x), then g(x)h(x)|f(x)h(x). (c) If h(x)|f(x) and h(x)|g(x), then h(x)|f(x) ± g(x). (d) If g(x)|f(x) and f(x)|g(x), then f(x) = kg(x) for some k ∈ F \ {0}

Let f (x) = ex - 4x2 a) Show that equation f (x) = 0 has...

Let f (x) = ex - 4x2 a) Show that equation f (x) = 0 has three real solutions. b) Use the Newton Method to calculate the largest of the solutions with precision. preset of 0.01.

Question1: Find the interval of increase and decrease of given function f(x)=3x^5-5x^3 f(x)=1/3 x^3-9x+2

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ). b True or False. The product of two increasing functions is increasing. Clarify your answer. c Find the point on the graph of f ( x ) = 4 − x 2 that is closest to the point ( 0 , 1 ).

Question

a) let f(x)= x^3-9x verify that on [-3,3] meets the requirements of rolle's therom, please show...

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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...

Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k

Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...

Given f(x)=2x3-7x2+9x-3, use the remainder theorem to find f(-1)

(abstract algebra) Let F be a field. Suppose f(x), g(x), h(x) ∈ F[x]. Show that the...

Let f (x) = ex - 4x2 a) Show that equation f (x) = 0 has...

Question1: Find the interval of increase and decrease of given function f(x)=3x^5-5x^3 f(x)=1/3 x^3-9x+2

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...