If \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\), then f(5) is _______.

The graph of y = e^x intersect the y-axis at _______.

Which one of the following functions has the property f (x) = \(f\left( \frac { 1 }{ x } \right) \), provided \(x \neq 0\)

The graph of f(x) = e^x is identical to that of ________.

\(\lim _{ x\rightarrow 0 }{ \frac { { e }^{ x }-1 }{ x } } =\)________.

Determine whether the following functions are odd or even?
f(x) = x + x²

Let f be defined by f(x) = x³ - kx² + 2x, x ∈ R,Find k, if 'f' is an odd function.

For \(f(x)=\frac { x-1 }{ 3x+1 } \) x > 1, write the expression of \(f\left( \frac { 1 }{ x } \right) \) and \(\frac { 1 }{ f(x) } \)

Evaluate \(\underset { h\rightarrow 0 }{ lim } \frac { \sqrt { x+h } -\sqrt { x } }{ h } \)

Differentiate (sec x -1) (sec x +1)

Differentiate sin² x with respect to x².

Evaluate the following \(\lim _{ x\rightarrow \infty }{ \frac { 2x+5 }{ { x }^{ 2 }+3x+9 } } \)

Find y₂ of the following function x = a cos \(\theta\), y = a sin \(\theta\)

Find \(\frac{dy}{dx}\) if x = 15(t - sin t); y = 18(1 - cos t).

If e^y (x + 1) = 1, show that \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }\)

Draw the graph of the following function f(x) = e^2x

Draw the graph of the following function f(x) = e^-2x

If \(\begin{matrix} \underset { x\rightarrow 1 }{ lim } & \frac { { x }^{ 4 }-1 }{ x-1 } \end{matrix}=\begin{matrix} \underset { x\rightarrow k }{ lim } & \frac { { x }^{ 3 }-{ k }^{ 3 } }{ { x }^{ 2 }-{ k }^{ 2 } } \end{matrix}\),then find the value of K

If \(x=a\left( t+\frac { 1 }{ t } \right) ;y=a\left( t-\frac { 1 }{ t } \right) \) show that \(\frac { dy }{ dx } =\frac { x }{ y } \)