Questions from General Calculus

Q: Prove that 1 + 3 + 5 + ∙∙∙ + (2n

Prove that 1 + 3 + 5 + ∙∙∙ + (2n - 1) = n2.

Q: If f0(x) = x2 and fn+1(

If f0(x) = x2 and fn+1(x) − f0(fn(x)) for n = 0, 1, 2, ..., find a formula for fn(x).

Q: a. If f0(x) = 1 / 2 -

a. If f0(x) = 1 / 2 - x and fn+1 = f0 0 fn for n = 0, 1, 2, ..., find an expression for fn(x) and use mathematical induction to prove it. b. Graph f0, f1, f2, f3 on the same screen and describe the e...

Q: One of the legs of a right triangle has length 4 cm

One of the legs of a right triangle has length 4 cm. Express the length of the altitude perpendicular to the hypotenuse as a function of the length of the hypotenuse.

Q: The altitude perpendicular to the hypotenuse of a right triangle is 12

The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.

Q: Solve the equation |2x - 1|-|x + 5|=

Solve the equation |2x - 1|-|x + 5|= 3.

Q: Find the domain of the function. /

Find the domain of the function.

Q: Solve the inequality |x - 1|-|x - 3|≥

Solve the inequality |x - 1|-|x - 3|≥ 5.

Q: Sketch the graph of the function f(x) = |

Sketch the graph of the function f(x) = |x2 - 4|x|+ 3|.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If x1 < x2 and f is a decreasing function, th...