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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
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
- 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_forwardThe process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits in Exercises 23–36.arrow_forwardIn Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and asymptotes.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_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_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
- Section 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_forwardUse 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_forward
- Section 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_forwardExercise 1: Show that Please show all work and a small explanation. lim x 1 (x 4 1)² = ∞arrow_forwardExample 48 lim,(Vx2 + x – Vx² + 5) =?arrow_forward
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