Determine order and degree (if defined) of differential equation y'''+2y''+y'=0
Determine order and degree (if defined) of differential equation (y''')2+(y'')3 +(y')4 +y5 =0
Determine order and degree (if defined) of differential equation \(\frac{d^2y}{dx^2}=\cos 3x+\sin3x\)
Determine order and degree (if defined) of differential equation\(\Big(\frac{d^2y}{dx^2}\Big)\\^2+\cos\Big(\frac{dy}{dx}\Big)=0\)
Determine order and degree(if defined) of differential equation\((\frac{ds}{dt})^4+3s\frac{d^2s}{dt^2}=0\)
Determine order and degree(if defined) of differential equation y'+5y-0
Verify A(adj A)=(adj A)A=\(\mid A \mid I\).
\(\begin{bmatrix}1&-1&2\\3&0&-2\\1&0&3\end{bmatrix}\)
By using properties of determinants, show that:
\(\begin{vmatrix}a^2+1&ab&ac\\ab&b^2+1&bc\\ca&cb&c^2+1\end{vmatrix}\)=1+a2+b2+c2
Show that the function defined by f(x)=cos(x2) is a continuous function.
Find the values of a and b such that the function defined by\(f(x)=\left\{\begin{matrix} 5, &if\,x\leq2 \\ ax+b,&if\,2<x<10 \\ 21,&if\,x\geq10 \end{matrix}\right.\)
is a continuous function.
Find the values of k so that the function f is continuous at the indicated point.\(f(x)=\left\{\begin{matrix} kx+1, &if\, x\leq\pi \\ cos\,x,&if\,x>\pi \end{matrix}\right.\,at\,x=\pi\)
Find the values of k so that the function f is continuous at the indicated point. \(f(x)=\left\{\begin{matrix} kx^2, &if\,x\leq2 \\ 3,&if\,x>2 \end{matrix}\right. \,at\,x=2\)
Find the values of k so that the function f is continuous at the indicated point. \(f(x)=\left\{\begin{matrix} \frac{k\,cos\,x}{\pi-2x}, &if\,x\neq\frac{\pi}{2} \\ 3,&if\,x=\frac{\pi}{2} \end{matrix}\right.at\, x=\frac{\pi}{2}\)
Examine the continuity of f, where f is defined by\(f(x)=\left\{\begin{matrix} sin\,x-cos\,x, &if\,x\neq0 \\ -1,& if\,x=0 \end{matrix}\right.\)
Determine if f is defined by\(f(x)=\left\{\begin{matrix} x^2sin\frac{1}{x}, &if\,x\neq0 \\ 0,&if\,x=0 \end{matrix}\right.\)is a continuous function?
Find the points of discontinuity of f, where\(f(x)=\left\{\begin{matrix} \frac{sin\,x}{x} &if\,x<0 \\ x+1& if\,x\geq0 \end{matrix}\right.\)
Discuss the continuity of the following functions.(a) f(x)=sinx+cosx(b) f(x)=sinx−cosx(c) f(x)=sinx\(\times\)cosx
Is the function defined by \(f(x)=x^2-sin\,x+5\) continuous at \(x=p\) ?
Show that the function defined by \(g(x)=x-[x]\) is discontinuous at all integral points. Here \([x]\) denotes the greatest integer less than or equal to \(x\).
For what value of λ is the function defined by\(f(x)=\left\{\begin{matrix} \lambda (x^2-2x) &if\,x\leq0 \\ 4x+1&if\,x>0 \end{matrix}\right.\)continuous at x=0? What about continuity at x=1?
Find the relationship between a and b so that the function f is defined byf(x)=\(\left\{\begin{matrix} ax+1 &if\,x\leq3 \\ bx+3&if\,x>3 \end{matrix}\right.\) is continuous at x=3.