The graph of y = 2x² is passing through _______.

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

The range of f(x) = |x|, for all \(x\in R\), is ________.

If the function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to ________.

If y = log x then y₂ = ________.

If \(f(x)=\frac { x+1 }{ x-1 } \) ,x ≠ 0 then prove that f(f(x)) = x

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

Find the derivative of the following functions from first principle. log (x + 1)

Differentiate \({ x }^{ \frac { 2 }{ 3 } }\) from first principles

Find \(\frac { dy }{ dx } \) if x² + xy + y² = 100

Find  \(\frac{dy}{dx}\)   of the following functions: x = a (θ - sin θ),y = a(1- cosθ)

Differentiate sin³ x with respect to cos³x.

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

Evaluate \(\underset { x\rightarrow -3 }{ lim } \frac { { x }^{ 3 }+27 }{ { x }^{ 5 }+243 } \)

Evaluate \(\underset { x\rightarrow 0 }{ lim } \frac { 2sinx-sin2x }{ { x }^{ 3 } } \)

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

Differentiate: \(\frac { sinx+cosx }{ sinx-cosx } \)with respect to 'x'

Find the derivate of (x³-27)from first principles.

Darw the graph of f(x) = log_ax; x > 0, a > 0 and \(a\ne 1\).