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Limits Worksheets. Limits. Basic. Substitution. 1.\:\:\lim _ {x\to 0} (\frac {1} {2}) 2.\:\:\lim _ {x\to 1} (2x^2-3x+5) 3.\:\:\lim _ {x\to 2} (x (x-3)) 4.\:\:\lim _ {x\to 3} (\frac {3-x} {x^2+2x}) 5.\:\:\lim _ {x\to -1} (\frac {x+1} {x-1})^2.
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.
13 Φεβ 2019 · 1. How do you read f(x)? Solution: \F" of \X." 2. How do you read lim f(x) = L? x!a. Solution: The limit of \F" as \X" approaches \A" is \L." 3. How do you read lim. x!a. f(x)? Solution: The limit of \F" as \X" approaches \A" from the left. 4. How do you read lim f(x)? x!a+. Solution: The limit of \F" as \X" approaches \A" from the right.
1. Find the limit (if it exists): 2. Describe the intervals on which the function is continuous: This function is discontinuous at x = 1 & x = −2 since then we get a 0 in the denominator. So, it is continuous on the intervals (−∞, −2) and (−2, 1) and (1, ∞) 3.
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 ...
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. Name___________________________________
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.
