If f is a quadratic function such that f(0) = 1 and integral f(x)/x^2(x + 1)^3...
Let f(x) be a quadratic function such that f(0)=?4 and ?f(x)/x2(x+3)^6dx is a rational function. Let f(x)| be a quadratic function such that f(0) = -4| and integral f(x) / x^2(x + 3)^6 dx| is a rational function. Determine the value of f'(0)|.
9, Bonus: (1 point) If f is a quadratic function such that f(0) = 1 and a2(x+1)3 is a rational function, find the value of f' (0)
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
Which quadratic function represents the data shown in the table? X -3 - 2 0 1 2. 3 y 20 0 -4 -4 0 1. f(x)= 2x2 – 2x - 4 II. f(x)= 2(x - 2)(x + 1) III. f(x)=2(x -0.5)2 - 4.5 O A. I only O B. ll only C. Ill only O D.I, II, and III
Evaluate the integral 1+2 2017 de Note: Use an upper-case "C" for the constant of integration. Let f(2) be a quadratic function such that f(0) = 6 and f(2) dac is a rational function. Determine the value of f'(o). f(0) =
Anti-differentiation Question 1. Find the function f(x) if 1. f'(x) = 0.5e -0.2x, f(0) = 0 2. f'(x) = x2 + Vx, f(1) = 3 3. f'(x) = 1 7x Question 2. Find the number k: 14t - +0 e 4x-1 2.[(4 – x)"dx = kin/4 – xl + c 3.5(3x+2)*dx = k(3x + 2)5+C
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
1. Numerical Integration The integral of a function f(x) for a s x S b can be interpreted as the area between the f(x) curve and the x axis, bounded by the limits x- a and x b. If we denote this area by A, then we can write A as A-f(x)dx A sophisticated method to find the area under a curve is to split the area into trapezoidal elements. Each trapezoid is called a panel. 1.2 0.2 1.2 13...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx