Engineering Mat...

What is the value of \( \mathop {\lim }\limits_{\theta \to \infty } \frac{1-cos2\theta}{\theta}~?\)

Compute the value of ​\(\begin{array}{*{20}{c}} {{\rm{lim}}}\\ {x \to 3} \end{array}\frac{{{x^3} - 125}}{{{x^2} - 8x +15}}\)

The values of x for which the function

\(f\left( x \right) = \frac{{{x^2} - 3x - 4}}{{{x^2} + 3x - 4}}\)

is NOT continuous are

If the value of  \(y =\mathop {\lim }\limits_{y \to \infty } {\left( {1 + \frac{1}{4x}} \right)^{x}}\)  then find y?

The value of \(\begin{array}{*{20}{c}}{{\rm{lim}}}\\{h \to 0}\end{array}\frac{{{2^{8cosh}}}}{{8h}}\left[ {{{\sin }^8}\left( {\frac{\pi }{6} + h} \right) - {{\sin }^8}\frac{\pi }{6}} \right]\)

Consider a function g(x) continuous at x = 0 where

\(g\left( x \right) = \frac{{({{128}^x} - {4^x})}}{{{a^x} - 1}}\;for\;x \ne 0\)

\( = 5\;for\;x = 0\)

What is the value of \(f\left( x \right) = \mathop {\lim }\limits_{x \to 1} \frac{{x + {x^2} + {x^3} + {x^4} + \ldots + {x^n} - n}}{{x - 1}}\)

Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x =0, f(x) is

If \(p = \begin{array}{*{20}{c}} {lim}\\ {x \to 0} \end{array}\;{\left( {1 + {{\tan }^2}\sqrt x } \right)^{\frac{1}{{2x}}}}\) Find ln p

Find the value of \(\mathop {{\rm{lim}}}\limits_{x \to 0\;} \frac{{{{({5^x} - 1)}^4}}}{{({7^x} - 1).sinx.\;{\rm{log}}\left( {1 + x} \right).tanx}}\)