(a) State the definition of the derivative of f. (b) Using (a), prove the following:d/dx(f(x) +g(x))...

(a) State the definition of the derivative of f.

(b) Using (a), prove the following:d/dx(f(x) +g(x)) =d/dx(f(x)) +d/dx(g(x))

Expert Solution

milcah answered 3 years ago

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) -...

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) - f(x)g'(x))/g^2(x)

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f...

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f '(x) = 6x + 5 Then, Find the tangent line of f(x) at x = 3 Finally, Find the average rate of change between x = −1 and x = 2

3.1.24 Prove that <f,g> = the integral f(x)*g(x)dx from 0 to 1 does not define an...

3.1.24 Prove that <f,g> = the integral f(x)*g(x)dx from 0 to 1 does not define an inner product on the vector space C0[-1,1]. Explain why this does not contradict the fact that it defines an inner product on the vector space C0[0,1]. Does it define an inner product on the subspace P(n) C C0[-1,1] consisting of all polynomial functions?

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 +...

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 + 6x (ln x) – 6x is an anti-derivative of (ln x)3 (must show all work)

a) State the definition that a function f(x) is continuous at x = a. b) Let...

a) State the definition that a function f(x) is continuous at x = a. b) Let f(x) = ax^2 + b if 0 < x ≤ 2 18/x+1 if x > 2 If f(1) = 3, determine the values of a and b for which f(x) is continuous for all x > 0.

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

a) use the sequential definition of continuity to prove that f(x)=|x| is continuous. b) theorem 17.3...

a) use the sequential definition of continuity to prove that f(x)=|x| is continuous. b) theorem 17.3 states that if f is continuous at x0, then |f| is continuous at x0. is the converse true? if so, prove it. if not find a counterexample. hint: use counterexample

Question

(a) State the definition of the derivative of f. (b) Using (a), prove the following:d/dx(f(x) +g(x))...

Solutions

Expert Solution

Related Solutions