calculus

Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=-3, f''(0)=1, and f'''(0)=4.

Write the third-degree Taylor polynomial for h, where h(x) = integral of f(t)dt from 0 to x, about x=0
for this part, I got 5x-3x^2/2+x^3/6.

Then the second part asks, Let h be defined as the part above. Given that f(1)=3, either find the exact value of h(1) or explain why it cannot be determined.
I am not understanding this part. Please help me out.

The Taylor polynomial for f(x) is 5 -3x + (1/2)*1*x^2 + (1/6)*4*x^4
The Taylor polynomial for h(x) is
5x -(3/2)x^2 + (1/6)x^3 + ...

It is not necessary from the f(0) derivatives provided that the value of f(1) be 3. That is additional information. Since the exact funtion has not been specified, the exact value of the integral from 0 to 1 caqnnot be specified either, even when f(0) and f(1) are known.

I agree that this is a very confusing question.

asked by Meredith

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    The function f has derivatives of all orders for all real numbers x. Assume f(2)=-3, f'(2)=5, f''(2)=3, and f'''(2)=-8. The fourth derivative of f satisfies the inequality, the (absolute value of f''''(x)) <=3 for all x in the
  2. Math

    Assume that f is a continuous function from the real numbers to the real numbers such that for all numbers x,y, and a it is true that f(x+y)=f(x) + f(y) and that f(ax)=af(x). Further assume that f(1) = pi. Find f'(-1). Please
  3. Pre-Calculus

    A rectangle is bounded by the x-axis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers
  4. Math

    The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a
  5. Math

    What is the domain and range fro the expentiral function f(x)=-2x4^x-1+3? Domain:all real numbers Range:all real numbers less than 3 Domain:all real numbers Range:all real numbers greater than 3 Domain: all real numbers greater
  6. Algebra 1-- Please, check my answers!

    1. What is ((-12x^6 + x)) / ((-4x^2))? A: 3x^4 - 1/4x 2. What is the greatest common factor of the terms of the polynomial 6x^3 - 18x^2 + 12x + 3? A: 3? 3. Which is a solution to n/n+2 = -8/n? a. -4 b. -2 c. 2 d. 4 A: a? 4. Which
  7. Math Algebra 1111

    If the domain of a function F is the set of all real numbers and the domain of a function G is the set of all real numbers, under what circumstances do (F+G)(x) and (F/G)(x) have different domains? Whenever G(x) = 0 then the
  8. Algebra

    The vertex of a parabola is at (-2,4), and the x-intercepts are at -6 and 2. Determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: all real numbers R: y ≤ 4 c. D: -6 ≤ x
  9. Algebra :P... again

    Hi! Sorry.. but 1 more question? Direction: Find the domain of the function. Problem: y = - 1 0 / 1 1 - x [A] All real numbers except x= -11 [B] All real numbers except x= 0 [C] All real numbers except x= 10 [D] All real numbers
  10. math 116

    What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a

More Similar Questions