What is \lim_{x\rightarrow 0}f(x) equal to?
Consider the following for the next two (02) items that follow: Let f(x)=\begin{cases}ax(x+1)+b,&x \lt 1\\ x-1,&1\le x\le2\end{cases}
- A. -\frac{1}{3}
- B. -\frac{2}{3} ✓
- C. 0
- D. 1
Correct Answer: B. -\frac{2}{3}
Explanation
Since we need the limit as x \rightarrow 0, we use the definition for x \lt 1: f(x) = ax(x+1)+b. Taking the limit as x \rightarrow 0, we get f(0) = a(0) + b = b. From the previous question's solution, b = -\frac{2}{3}. Therefore, the limit is -\frac{2}{3}.
Related questions on Calculus
- Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
- If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
- What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
- What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?