Using the function, f(x) = 3 - x, find the following: (a) f(x+h) (b) f(x+h)-f(x) f(x+h)-f(x) (c) h f(x+h) = f(x+h)-f(x) = (Simplify your answer.) f(x+h)-f(x) h (Simplify your answer.) b
Determine the difference quotient f(x+h)-f(x) h f(x) = 5x?- 8 f(x+h)-f(x) h (Simplify your answer. Do not factor.)
Added the formulas, thank you! Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered difference for 1st derivative s(a) (3) 2h t)-2e-bCentered diference for 2nd derivative (4) 2 2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f"(1) for f(x)e with h 1, 2-1, 2-2,.., 2-60. Format your output in columns as follows: h (6+f)() error (öf(1 error f error Indicate the...
1. Calculate f(x + h) 2. Calculate f (x+h)-f(x) 3. Simplify f(a+h)-f(x) 4. finish up with the limit Given f(x) = x2 - 12x, use lim f(x + h) - f(x) to find the slope of a tangent line this this function when x= 3. h
f(x+h)-f(x) 12. Determine lim h 0 h a. f(x)= x² answer: 2x 1 b. f(x)= x answer: 2√x c. f(x)=1/ x answer: -1/x? d. f(x)= et answer: et e. f(x) = sin x answer: COS X f. f(x)= = COS X answer: – sin x
f(x+h)-f(x) Find the difference quotient h where h = 0, for the function below. f(x) = 2x-3 Simplify your answer as much as possible. f(x + n) - f(x) h Х $ ?
h h-0 f(x +h) – f(x) a. For the following function, find f using the definition f'(x) = lim b. Determine an equation of the line tangent to the graph off at (a,f(a)) for the given value of a. f(x) = (3x +7, a = 6
For the function f(x) = - 8x, compute the following (for h70). f(x +h)-f(x) a. f(x + h); b. f(x +h)-f(x); c. h a. f(x+h) = (Simplify your answer.) b. f(x + h) – f(x) = (Simplify your answer.) c. f(x +h)-f(x) h (Simplify your answer.)
Let h : X −→ Y be defined by h(x) := f(x) if x ∈ F g −1 (x) if x ∈ X − F Now we must prove that h is injective and bijective. Starting with injectivity, let x1, x2 ∈ X such that h(x1) = h(x2). Assume x1 ∈ F and x2 ∈ X −F. Then h(x1) = f(x1) ∈ f(F) and h(x2) = g −1 (x2) ∈ g −1 (X − F) = Y...
f(x +h)-f(x) By determining f'(x) = lim h h0 find f'(5) for the given function. f(x) = 6x2 f'(5)=(Simplify your answer.)