Related InterviewSolutions

• If `f(x)=2x-|x|`, then at `x=0`A. f is continuousB. f is discontinuousC. `underset(x rarr 0^(-))lim f(x)=3`D. `underset(x rarr 0^(+))lim f(x)=1`
• If `f(x)={:{((x)/(|x|)", for " x!=0),(c", for " x=0):}`, then f isA. continuous at `x=0`B. discontinuous at `x=0`C. continuous if `f(0)=1`D. continuous if `f(0)=-1`
• Identify discontinuities if any for the following functions as either a jump or a removable discontinuity on their respective domains.f(x) = x2 + 5x + 1, for 0 ≤ x ≤ 3 = x2 + x + 5, for 3 < x ≤ 6
• If `f(x)=a^(x), a gt 0`, then f isA. continuous for all `x in R^(+)`B. continuous for all `x in R^(-)`C. continuous for all ` x in R`D. discontinuous for all ` x in R`
• The rational function `f(x)=(g(x))/(h(x)), h(x) != 0` isA. continuousB. discontinuous for integer values onlyC. continuous for integer values onlyD. continuous for imaginary values only
• Discuss the continuity of the function `log_c x,` where `c> 0, x > 0.`A. continuous in `(-oo, oo)`B. continuous in `(0, oo)`C. discontinuous in `(-oo, oo)`D. discontinuous in `(0, oo)`
• Examine the continuity of the given function at given points `f(x)=(x+3x^2+5x^3+.....+(2n-1)x^n-n^2)/(x-1)`, for `x != 1` at `x=1 and =(n(n^2-1))/3`,for `x=1`A. `(n(n+1)(2n-1))/(6)`B. `(n(n+1)(2n-1))/(3)`C. `(n(n+1)(4n-1))/(6)`D. `(n(n+1)(4n-1))/(3)`
• If \(f(x) =\begin{cases}x\,sin \frac{1}{x}, & \quad x\neq 0\\k, & \quad x=0\end{cases}\) is continuous at x = 0, then the value of k =f(x) = {x sin(1/x), x ≠ 0, k, x = 0 is continuous at x = 0, then the value of k(A) 1(B) –1(C) 0(D) 2
• Prove that \(f(x) = \begin{cases} 2-x, & \quad \text{when x <2;} \text{}\\ 2+x, & \quad \text{whenx≥2} \end{cases}\)  is discontinuous at x=2
• Prove that  \(f(x) = \begin{cases} 3-x, & \quad \text{when x ≤0;} \text{}\\ x^2, & \quad \text{whex>0} \end{cases}\)  is discontinuous at x = 0