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# Popular Questions - Calculus

## What are continuous functions?

We may also state two alternative definitions of , using either the sequential criterion or else using topology and open sets. Alternative definition number 1 Let ##f: X ->Y## be a function and let...

## What is the limit as x approaches 0 of ##arctan(ln(x))##?

Since ##lim_(x->0^+)lnx=-oo## hence we have that ##lim_(x->-oo)arctanx=-pi/2##

## What is Infinity?

It depends on the context… ##bb +-## Infinity and limits Consider the set of Real numbers ##RR##, often pictured as a line with negative numbers on the left and positive numbers on the right....

## How do you use part 1 of Fundamental Theorem of Calculus to find the derivative of the function ##y=int (6+v^2)^10 dv## from sinx to cosx?

##[-(6+cos^2x)^10 sinx – (6+sin^2x)^10 cosx]## If it is F(v) = ##int_sinx^cosx (6+v^2)##dv, it can be written as a sum of two integrals= ##int_sinx^0 (6+v^2)dv## +##int_0^cosx (6+v^2)dv##...

## How do you find the second derivative of ##sec^2 (2x)##?

By definition, ##sec^2(u) = (1 + tan(u))## Considering, in our case, ##u = 2x##, we can derive your function as follows: ##(dy)/(du) = 0 + u’*sec^2(u)## Deriving a constant (number ##1##)...

## What is the taylor series of ##xe^x##?

aaaah now here’s a fun question. I kinda wanna thank you for asking it! Here’s my answer, if you just want this in a rush: If ##f(x) = xe^x##, then you can actually write an exact sum:...