Engineering Mat...

1 + x + x²/2 – x⁴/8 – x⁵/15 + … =

In the Taylor series expansion of ln x about x = 1, the coefficient of (x - 1)⁴ is

According to the Mean Value Theorem, for a continuous function f(x) in the interval [a, b], there exists a value ξ in this interval such that \(\mathop \smallint \limits_a^b f\left( x \right)dx =\)

If z = e^xsiny, x = log_et and y = t² then \(\frac{{dz}}{{dt}}\)is given by the expression

Consider a function f = y^x, then the value of \(\left( {\frac{{{\partial ^2}f}}{{\partial x\partial y}}} \right)\) at point (2, 1) is -

If \(U = \log \left( {{x^3} + {y^3} - {x^2}y - {y^2}x} \right)\), evaluate \(\frac{{{\partial ^2}U}}{{\partial {x^2}}} + \frac{{2{\partial ^2}U}}{{\partial x\partial y}} + \frac{{{\partial ^2}U}}{{\partial {y^2}}}\)

The maximum value of the function \(f\left( x \right) = - \frac{5}{3}{x^3} + 10{x^2} - 15x + 16\) in the interval (0.5, 3.5) is 

Find the value of ‘c’ lying between a = 0 and b = ½ in the Mean Value Theorem for the function f(x) = x(x - 1)(x - 2)