Questions from General Calculus

Q: Find all functions f such that f is continuous and /

Find all functions f such that f is continuous and

Q: A student forgot the Product Rule for differentiation and made the mistake

A student forgot the Product Rule for differentiation and made the mistake of thinking that / However, he was lucky and got the correct answer. The function f that he used was / and the domain of his...

Q: Let f be a function with the property that f(0

Let f be a function with the property that f(0) = 1, f’(0) = 1, and f(a+b) = f(a) f(b) for all real numbers a and b. Show that / for all x and deduce that /

Q: Find all functions f that satisfy the equation /

Find all functions f that satisfy the equation

Q: Find the curve y = f(x) such that f

Find the curve y = f(x) such that f(x) > 0, f(0) − 0, f(1) = 1, and the area under the graph off from 0 to x is proportional to the (n + 1)st power of f(x).

Q: A sub tangent is a portion of the x-axis that

A sub tangent is a portion of the x-axis that lies directly beneath the segment of a tangent line from the point of contact to the x-axis. Find the curves that pass through the point (c, 1) and whose...

Q: Calculate 20 or 30 terms of the sequence for p0 =

Calculate 20 or 30 terms of the sequence for p0 = 1 2 and for two values of k such that 1 < k < 3. Graph each sequence. Do the sequences appear to converge? Repeat for a different value of p0 betwe...

Q: Use the Ratio Test to determine whether the series is convergent or

Use the Ratio Test to determine whether the series is convergent or divergent.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Use the Ratio Test to determine whether the series is convergent or

Use the Ratio Test to determine whether the series is convergent or divergent.