Two-Sided vs. One-Sided Limits
Read this topicProblems 4
- Define f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R as follows: f(x)={2x+5x<−2x2−2≤x<13x−11≤x<30x=311−2x33<xf(x) = \begin{cases} 2x+5 & x < -2 \\ x^2 & -2 \le x < 1 \\ 3^{x-1} & 1 \le…
- Define a function fff as follows. f(x)=0f(x) = 0f(x)=0 for all x≤0x \le 0x≤0. For all k∈Zk \in \mathbb{Z}k∈Z (integers), if x∈[2k,2k+1)x \in [2^k, 2^{k+1})x∈[2k,2k+1), then f(x)…
- f(x)={3xx≤2−2x+8x>2f(x) = \begin{cases} 3x & x \le 2 \\ -2x + 8 & x > 2 \end{cases}f(x)={3x−2x+8x≤2x>2 What is limx→2f(x)\lim_{x \to 2} f(x)limx→2f(x)?
- A continuous function f(x) is defined as 3x+43x + 43x+4 when x>0x > 0x>0, and x2+Cx^2 + Cx2+C when x<0x < 0x<0, where C is some constant. What is C?