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Find an example of a function such that the limit exists at every x, but that has an in nite number of discontinuities. (You can describe the function and/or write a
Evaluate this limit using the Limit Laws. Show each step. lim (1 + √3) (2 − 9 2 + 3) →. Solution: Using the Limit Laws, rewrite the limit. lim (1 + √3) (2 − 9 2 + 3) = [lim1 + lim√3] ∙ [lim2 − lim9 2 + lim 3] → →8 →8 →8 →8 →8. = [lim1 + 3 ] ∙ [lim2 − 9 (lim)2+ (lim)3] √lim. → →8 →8 →8 →8.
CALCULUS AB WORKSHEET 1 ON LIMITS. Work the following on notebook paper. No calculator. 1. The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does not exist, explain why. ( a ) lim ⎡ ⎣ f ( x g ( x. x → 2. ( ) c lim ⎡ f x g x ⎤. x → 0 ⎣ ( ) ( ) ⎦. ( b ) lim f. → 1 ⎡ ⎣ ( x g ( x ) ⎤ ⎦. ( x ) lim ( )
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.
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___________________________________
Limits are a very powerful tool in mathematics and are used throughout calculus and beyond. The key idea is that a limit is what I like to call a \behavior operator". A limit will tell you the behavior of a function nearby a point.
