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Estimating Limits In Exercises 1–4, use a graphing utility to graph the function and visually estimate the limits.
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Chapter 2 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- In Exercises 79–82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.) 79. lim f(x) = 0, lim f(x) = ∞, and lim f(x) = ∞ x→too x-2+ 80. lim g(x) = 0, lim g(x) = –∞, and lim g(x) = ∞ x→3- x→3* 81. lim h(x) = -1, lim h(x) = 1, lim h(x) = -1, and x -00 lim h(x) = 1 x→0+ 1, lim k(x) x→l¯ = 00, and lim k(x) x→I* 82. lim k(x) = -00arrow_forwardIn Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and asymptotes.arrow_forwardFind the natural domain and graph the functions in Exercises 15–20.15. ƒ(x) = 5 - 2x 16. ƒ(x) = 1 - 2x - x217. g(x) = sqrt( | x | ) 18. g(x) = sqrt(-x)19. F(t) = t/ | t | 20. G(t) = 1/ | t |arrow_forward
- In Exercises 1–4, show that the limit leads to an indeterminate form. Then carry out the two-step procedure: Transform the function alge- braically and evaluate using continuity.arrow_forwardSection 2-2 : The Limit 8-x 1. For the function f (x)= x² -4 answer each of the following questions. (a) Evaluate the function the following values of x compute (accurate to at least 8 decimal places). (i) 2.5 (vi) 1.5 (ii) 2.1 (vii) 1.9 (iii) 2.01 (viii) 1.99 (iv) 2.001 (ix) 1.999 (v) 2.0001 (x) 1.9999 8-x (b) Use the information from (a) to estimate the value of lim x2 x -4 2-Vr +3 2. For the function R(t)= answer each of the following questions. t+1 (a) Evaluate the function the following values of t compute (accurate to at least 8 decimal places). (i) -0.5 (vi) -1.5 (ii) -0.9 (vii) -1.1 (iii) -0.99 (viii) -1.01 (iv) -0.999 (ix) -1.001 (v) -0.9999 (x) -1.0001 -VP +3 (b) Use the information from (a) to estimate the value of lim t+1 sin (70) 3. For the function g(0)3= answer each of the following questions. (a) Evaluate the function the following values of 0 compute (accurate to at least 8 decimal places). Make sure your calculator is set to radians for the computations. (iii) 0.01…arrow_forwardIn Exercises 4–18,(evaluate the limit)or explain why it does not exist. 4. lim (x² – 4x + 1) 5. lim x 3 x + 6 x + 3 X4arrow_forward
- Use the given graph of f to state the value of each quantity, if it exists. (If it does not exist, enter NONE. a) lim x→3− f(x) b) im x→3+ f(x) c) lim x→3 f(x) d) lim x→7 f(x) e) f(7)arrow_forwardWhat is the sign of a if f (x) = ax³ +x +1 satisfies lim f(x) = o0? X -00 %3|arrow_forwardSection 2-2 : The Limit 8-x 1. For the function f (x) = x? - 4 answer each of the following questions. (a) Evaluate the function the following values of x compute (accurate to at least 8 decimal places). (i) 2.5 (vi) 1.5 (ii) 2.1 (vii) 1.9 (iii) 2.01 (viii) 1.99 (iv) 2.001 (ix) 1.999 (v) 2.0001 (x) 1.9999 8-x' (b) Use the information from (a) to estimate the value of lim- I+2 x -4 2-V +3 2. For the function R(t)= answer each of the following questions. %3D t+1 (a) Evaluate the function the following values oft compute (accurate to at least 8 decimal places). (i) -0.5 (vi) -1.5 (ii) -0.9 (vii) -1.1 (iii) -0.99 (vii) -1.01 (iv) -0.999 (ix) -1.001 (v) -0.9999 (x) -1.0001 2-Vi? +3 (b) Use the information from (a) to estimate the value of lim t+1 sin (70) 3. For the function g (0) answer each of the following questions. (a) Evaluate the function the following values of 0 compute (accurate to at least 8 decimal places). Make sure your calculator is set to radians for the computations. (i)…arrow_forward
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