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True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x| is not...

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Basic Math

True and False (No need to solve).

1. Every bounded continuous function isintegrable.

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

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

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

5. The total areas of step function, f(k)=k feet, for k rangingfrom 1 to 1000 is 500.50 ft2, assuming each step has awidth 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 rangingfrom 1 to 1000 is 550 ft2, assuming each step has awidth of 1 foot.

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