(v) The value of \( \int_{-\infty}^{\infty} \delta(t) d t \) is: (a) 0 (b) 1 (c) -1 (d) \( \infty \) (vi) Solution of \( \frac{d^{2} x}{d x^{2}}-k x=0 \), when \( k=0 \) is: (a) \( c_{1} x+c_{2} \) (b) \( c_{1} \cos x+c_{2} \sin x \) (c) \( c_{1} e^{\lambda x}+c_{2} e^{-\lambda x} \) (d) None of these (vii) Equation \( u_{t u}-c^{2} u_{x z}=0 \) is: (a) one dimensional wave equation P.T.O.

\( \left\{\begin{array}{l}f(x)=x^{2}-1 \\a=1 \\\lim _{h \rightarrow 0} (\frac{f(a+h-f(a)}{h}\end{array}\right. \)

1) si \( \left(x^{2}+y^{2}\right)^{2}+3 x y-y^{2}=0 \quad \) halle \( \frac{d y}{d x} \left\lvert\,\left(\frac{1}{2},-\frac{1}{2}\right)\right. \)

\( y = ( 4 x ^ { 2 } - 2 x + 6 ) ( x ^ { 2 } + 6 x - 3 ) \quad y ^ { \prime } = \)

\( \left. \begin{array} { l l } { u = x ^ { 2 } + 3 x + 2 } & { u ^ { \prime } = 2 x + 3 } \\ { v = x - 1 } & { v ^ { 3 } = 1 } \\ { } & { ( 2 x + 3 ) ( x - 1 ) - ( x ^ { 2 } + 3 x ) 2 ) ( 1 ) } \end{array} \right. \)

implications. 10. Deseribe how vector calculas is utilized in electromagnetiom, specif- eally in calculating electric flelds.