The graph of f is given. (a) Find each limit, or explain why it does not exist. (i) lim x → 2 + f ( x ) (ii) lim x → − 3 + f ( x ) (iii) lim x → − 3 f ( x ) (iv) lim x → 4 f ( x ) (v) lim x → 0 f ( x ) (vi) lim x → 2 − f ( x ) (vii) lim x → ∞ f ( x ) (viii) lim x → − ∞ f ( x ) (b) State the equation of the horizontal asymptotes. (c) State the equations of the vertical asymptotes. (d) At what numbers is f discontinuous? Explain.
The graph of f is given. (a) Find each limit, or explain why it does not exist. (i) lim x → 2 + f ( x ) (ii) lim x → − 3 + f ( x ) (iii) lim x → − 3 f ( x ) (iv) lim x → 4 f ( x ) (v) lim x → 0 f ( x ) (vi) lim x → 2 − f ( x ) (vii) lim x → ∞ f ( x ) (viii) lim x → − ∞ f ( x ) (b) State the equation of the horizontal asymptotes. (c) State the equations of the vertical asymptotes. (d) At what numbers is f discontinuous? Explain.
Solution Summary: The author explains the limits of each of the given functions and if the limit does not exist.
Consider the function f(x), whose graph is shown below. Determine the limit of a function, by observing the behavior of the graph.
1. lim f(x) as x approaches to -5
2. lim f(x) as x approaches to -3
3. lim f(x) as x approaches to -2
4. lim f(x) as x approaches to -1
5. lim f(x) as x approaches to 3
(a) Estimate the value of
lim
x→ - infinity square root x^2+x+1 +1
by graphing the function f(x)=square root x^2+x+1 +1
b) use a table of values of f(x) to guess the value of the limit.
(a) Use a graph of
______________ ______________f(x) = √3 x2 + 8x + 6 - √3 x2 + 3x + 1
to estimate the value of lim x->∞ f(x) to one decimalplace.(b) Use a table of values of f(x) to estimate the limit tofour decimal places.(c) Find the exact value of the limit.
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