Examine the continuity of the function f (x) = x²+5 at x = -1

Give an example of a function which is continuous at x = 1, but not differentiable at x = 1.

Show that the function f (x) = \(\begin{cases} { x }^{ 3 }+3\quad ,\quad if\quad x\neq 0 \\ 1\quad \quad \quad ,\quad if\quad x=0 \end{cases}\) is not continuous at x = 0. 

If y= sec^-1 \(\left( \frac { \sqrt { x } +1 }{ \sqrt { x } -1 } \right) + sin^{ -1 }\left( \frac { \sqrt { x } -1 }{ \sqrt { x } +1 } \right) ,\ find\frac { dy }{ dx } .\)

If y = 500 e^7x + 600 e^-7x, show that \(\frac { d^{ 2 }y }{ dx^{ 2 } } =49y\).

if y = \(f({ e }^{ { { sin }^{ -1 } } }2x)\), find dy/dx.

If y = tan^-1\(\sqrt { \frac { 1-x }{ 1+x } } find\frac { dy }{ dx } \)

If y = a^x +x^a+x^x+a^a, find dy/dx

Show that the function f given by:
\(f(x)=\begin{cases} { x }^{ 3 }+3,\quad \quad \quad if\quad x\neq 0 \\ 1,\quad \quad \quad \quad \quad \quad if\quad x=0 \end{cases}\)
is not continuous at x = 0.

Show that the function defined by:
\(f(x)=\left| 1-x+\left| x \right| \right| ,\)
where x is any real number, is a continuous function.

Differentiate \({ x }^{ sinx\quad },x>0\quad w.r.t.\quad x.\)

Find the value of a for which the function f defined by

\(f(x)=\begin{cases} a\quad sin\frac { \pi }{ 2 } (x+1)\quad \quad ,\quad x\le 0 \\ \frac { tan\quad x\quad -\quad sin\quad x }{ { x }^{ 3 } } \ \ \ \ ,\quad x>0 \end{cases}\) is continuous at x = 0. 

Find \(\frac { dy }{ dx } \) if \(y=e^{ sin^{ 2 } }x\left\{ 2tan^{ -1 }\sqrt { \frac { 1-x }{ 1+x } } \right\} \)