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201-103-RE - Calculus 1 WORKSHEET: LIMITS 1. Use the graph of the function f(x) to answer each question. Use 1, 1 or DNEwhere appropriate. (a) f(0) = (b) f(2) = (c) f(3) = (d) lim x!0 f(x) = (e) lim x!0 f(x) = (f) lim x!3+ f(x) = (g) lim x!3 f(x) = (h) lim x!1 f(x) = 2. Use the graph of the function f(x) to answer each question. Use 1, 1 or ...
Introduction to Differential Equations. Separable Equations. Exponential Growth and Decay. Free Calculus worksheets created with Infinite Calculus. Printable in convenient PDF format.
Limits. Basic. Divergence. 1.\:\:\lim _ {x\to 0} (\frac {1} {x}) 2.\:\:\lim _ {x\to 5} (\frac {10} {x-5}) 3.\:\:\lim _ {x\to 1} (\frac {x} {x-1}) 4.\:\:\lim _ {x\to -2} (\frac {1} {x+2}) 5.\:\:\lim _ {x\to 5} (\frac {x} {x^2-25}) 6.\:\:\lim _ {x\to 2}\frac {|x-2|} {x-2}
Notice that the limits on this worksheet can be evaluated using direct substitution, but the purpose of the problems here is to give you practice at using the Limit Laws.
Kuta Software - Infinite Calculus. Evaluating Limits. Evaluate each limit. 1) lim 5. x→−1. 5. 3) lim ( x3 − x2 − 4) x→2. 0. 5) lim − x + 3. x→3. − 6. x − 4. 7) lim −. x→1. x2 − 6 x + 8. 1. 9) lim sin ( x) x→ π. 0. Critical thinking questions: 11) Give an example of a limit that evaluates to 4. Many answers. Ex: lim x. x→4.
Example 1: lim. 𝑥𝑥→−1. 𝑓𝑓(𝑥𝑥) = 2 lim. 𝑥𝑥→1. 𝑓𝑓(𝑥𝑥) = 4 lim. 𝑥𝑥→1. 𝑔𝑔(𝑥𝑥) = 6. The table above gives selected limits of the functions 𝑓𝑓 and 𝑔𝑔.
LIMITS BY STANDARD EXPANSIONS. Write down the first two non zero terms in the expansions of sin3x and cos2x . Hence find the exact value of. 3 x cos2 x − sin3 x . lim 3 . x → 0 3 x . sin3 x ≈ 3 x − 9 x 3 , cos2 x ≈ 1 − 2 x 2 , − 1. 2 2. Use standard expansions of functions to find the value of the following limit.
