WB1.1 - Limits and Directional Limits

Last updated over 5 years ago

6 questions

Question 1

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WB1.1 - Limits and Directional Limits

Last updated over 5 years ago

6 questions

Question 1

Find the \lim\limits_{x\to 2^-} f(x), \lim\limits_{x\to 2^+} f(x), \lim\limits_{x\to 2} f(x) of
f(x)=\begin{cases} \frac{x}{2}+\frac{1}{2}, & x\leq 2 \\ -\frac{x}{2}+\frac{3}{2}, & x>2 \end{cases}

Question 2

Find the \lim\limits_{x\to \frac{3}{2}^-} f(x), \lim\limits_{x\to \frac{3}{2}^+} f(x), \lim\limits_{x\to \frac{3}{2}} f(x) of f(x)=\begin{cases} -2x+1, & x\leq \frac{3}{2} \\ 2x-5, & x> \frac{3}{2} \end{cases}

Question 3

Find the \lim\limits_{x\to -3^-} f(x), \lim\limits_{x\to -3^+} f(x), \lim\limits_{x\to -3} f(x) of f(x)=\begin{cases} -x^2-10x-24, & x<-3 \\ \frac{x}{2}-\frac{3}{2}, & x\geq -3 \end{cases}

Question 4

Find the \lim\limits_{r\to 0^-} f(r), \lim\limits_{r\to 0^+} f(r), \lim\limits_{r\to 0} f(r) of f(r)=\begin{cases} r+1, & r<0 \\ r^2-2r+1, & r\geq 0 \end{cases}

Question 5

Find the following limits based on the graph: \lim\limits_{x\to -4^-} f(x), \lim\limits_{x\to -4^+} f(x), \lim\limits_{x\to 2} f(x) and \lim\limits_{x\to 4} f(x).

Question 6

Find the following limits based on the graph: \lim\limits_{x\to -2^-} g(x), \lim\limits_{x\to -2^+} g(x), \lim\limits_{x\to 1} g(x) and \lim\limits_{x\to 3} g(x).

Find the \lim\limits_{x\to 2^-} f(x), \lim\limits_{x\to 2^+} f(x), \lim\limits_{x\to 2} f(x) of 
f(x)=\begin{cases} 
      \frac{x}{2}+\frac{1}{2}, & x\leq 2 \\
      -\frac{x}{2}+\frac{3}{2}, & x>2
   \end{cases} 

Question 2

Find the \lim\limits_{x\to \frac{3}{2}^-} f(x), \lim\limits_{x\to \frac{3}{2}^+} f(x), \lim\limits_{x\to \frac{3}{2}} f(x) of f(x)=\begin{cases} -2x+1, & x\leq \frac{3}{2} \\ 2x-5, & x> \frac{3}{2} \end{cases}

Question 3

Find the \lim\limits_{x\to -3^-} f(x), \lim\limits_{x\to -3^+} f(x), \lim\limits_{x\to -3} f(x) of f(x)=\begin{cases} -x^2-10x-24, & x<-3 \\ \frac{x}{2}-\frac{3}{2}, & x\geq -3 \end{cases}

Question 4

Find the \lim\limits_{r\to 0^-} f(r), \lim\limits_{r\to 0^+} f(r), \lim\limits_{r\to 0} f(r) of f(r)=\begin{cases} r+1, & r<0 \\ r^2-2r+1, & r\geq 0 \end{cases}

Question 5

Find the following limits based on the graph: \lim\limits_{x\to -4^-} f(x), \lim\limits_{x\to -4^+} f(x), \lim\limits_{x\to 2} f(x) and \lim\limits_{x\to 4} f(x).

Question 6

Find the following limits based on the graph: \lim\limits_{x\to -2^-} g(x), \lim\limits_{x\to -2^+} g(x), \lim\limits_{x\to 1} g(x) and \lim\limits_{x\to 3} g(x).

WB1.1 - Limits and Directional Limits

WB1.1 - Limits and Directional Limits

Find the \lim\limits_{x\to 2^-} f(x), \lim\limits_{x\to 2^+} f(x), \lim\limits_{x\to 2} f(x) of f(x)=\begin{cases} \frac{x}{2}+\frac{1}{2}, & x\leq 2 \\ -\frac{x}{2}+\frac{3}{2}, & x>2 \end{cases}

Find the \lim\limits_{x\to \frac{3}{2}^-} f(x), \lim\limits_{x\to \frac{3}{2}^+} f(x), \lim\limits_{x\to \frac{3}{2}} f(x) of f(x)=\begin{cases} -2x+1, & x\leq \frac{3}{2} \\ 2x-5, & x> \frac{3}{2} \end{cases}

Find the \lim\limits_{x\to -3^-} f(x), \lim\limits_{x\to -3^+} f(x), \lim\limits_{x\to -3} f(x) of f(x)=\begin{cases} -x^2-10x-24, & x<-3 \\ \frac{x}{2}-\frac{3}{2}, & x\geq -3 \end{cases}

Find the \lim\limits_{r\to 0^-} f(r), \lim\limits_{r\to 0^+} f(r), \lim\limits_{r\to 0} f(r) of f(r)=\begin{cases} r+1, & r<0 \\ r^2-2r+1, & r\geq 0 \end{cases}

Find the following limits based on the graph: \lim\limits_{x\to -4^-} f(x), \lim\limits_{x\to -4^+} f(x), \lim\limits_{x\to 2} f(x) and \lim\limits_{x\to 4} f(x).

Find the following limits based on the graph: \lim\limits_{x\to -2^-} g(x), \lim\limits_{x\to -2^+} g(x), \lim\limits_{x\to 1} g(x) and \lim\limits_{x\to 3} g(x).

Find the \lim\limits_{x\to \frac{3}{2}^-} f(x), \lim\limits_{x\to \frac{3}{2}^+} f(x), \lim\limits_{x\to \frac{3}{2}} f(x) of f(x)=\begin{cases} -2x+1, & x\leq \frac{3}{2} \\ 2x-5, & x> \frac{3}{2} \end{cases}

Find the \lim\limits_{x\to -3^-} f(x), \lim\limits_{x\to -3^+} f(x), \lim\limits_{x\to -3} f(x) of f(x)=\begin{cases} -x^2-10x-24, & x<-3 \\ \frac{x}{2}-\frac{3}{2}, & x\geq -3 \end{cases}

Find the \lim\limits_{r\to 0^-} f(r), \lim\limits_{r\to 0^+} f(r), \lim\limits_{r\to 0} f(r) of f(r)=\begin{cases} r+1, & r<0 \\ r^2-2r+1, & r\geq 0 \end{cases}

Find the following limits based on the graph: \lim\limits_{x\to -4^-} f(x), \lim\limits_{x\to -4^+} f(x), \lim\limits_{x\to 2} f(x) and \lim\limits_{x\to 4} f(x).

Find the following limits based on the graph: \lim\limits_{x\to -2^-} g(x), \lim\limits_{x\to -2^+} g(x), \lim\limits_{x\to 1} g(x) and \lim\limits_{x\to 3} g(x).

Find the \lim\limits_{x\to 2^-} f(x), \lim\limits_{x\to 2^+} f(x), \lim\limits_{x\to 2} f(x) of
f(x)=\begin{cases} \frac{x}{2}+\frac{1}{2}, & x\leq 2 \\ -\frac{x}{2}+\frac{3}{2}, & x>2 \end{cases}