True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x|...

True and False (No need to solve).

1. Every bounded continuous function is integrable.

2. f(x)=|x| is not integrable in [-1, 1] because the function f is not differentiable at x=0.

3. You can always use a bisection algorithm to find a root of a continuous function.

4. Bisection algorithm is based on the fact that If f is a continuous function and f(x₁) and f(x₂) have opposite signs, then the function f has a root in the interval (x₁, x₂). As a consequence, one can infer that if a continuous function f(x) has a root at x=a, then there exists a number h such that f(a- h) and f(a+ h) have opposite sign.

5. The total areas of step function, f(k)=k feet, for k ranging from 1 to 1000 is 500.50 ft², assuming each step has a width of 1 foot.

6. if f is continuous then d/dx (integral(from a to x) f(t)dt= f(x).

7. The total areas of step function, f(k)=k feet, for k ranging from 1 to 1000 is 550 ft², assuming each step has a width of 1 foot.

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Expert Solution

milcah answered 1 year ago

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