Verify whether the following statements are true or false : (i) If :…

Question

Verify whether the following statements are true or false :

(i) If : $z = \frac{x^2 + y^2}{x - y}$, then : $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = 0$.

(ii) The curve $x^2 y^2 - x^2 + y^2 = 1$ has three asymptotes.

(iii) The area of a loop of the curve $r^2 = a^2 \cos 2\theta$ is $\frac{1}{2} a^2$.

(iv) $\text{erf}_c(x) = 1 - \text{erf}(x)$

(v) $\sinh^2 z + \cosh^2 z = 1$

(vi) Two non-zero vectors are perpendicular if their dot product is zero.

(vii) The gradient of a constant function is zero.

(viii) The differential equation $(D^3 - D)y = 0$ has two only solutions $e^x$ amd $e^{-x}$.

(ix) The P.I. of $(D - 3)^2 y = 2e^{3x}$ is $x^2 e^{3x}$.

(x) $\int_{0}^{2} \int_{0}^{3} (x + y) \, dx \, dy = 15$.

Related pages

• Euler's Theorem on Homogeneous Functions — topic
• Engineering Mathematics-I syllabus

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