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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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Calculus
- In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16arrow_forwardIn Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and asymptotes.arrow_forwardExercises 111-114: Determine the domain and range of function f. Use interval notation. 111. f(x) = =(x + 1)² – 5 112. f(x) = 2(x – 5)² + 10 113. f(x) = V-x – 4 – 2 114. f(x) = -Vx – 1 + 3arrow_forward
- Exercises 35–42: Write the given expression in the form f(x) = a(x – h)² + k. Identify the vertex. 35. f(x) = x² - 3x 36. f(x) = x² – 7x + 5 37. f(x) = 2x² – 5x + 3 38. flx) = 3x² + 6x + 2 39. f(x) = 2x² – &x – 1 40. f(x) = --² - x 41. f(x) = 2 – 6x – 3x 42. f(x) = 6 + 5x – 10x?arrow_forwardIn Exercises 43 and 44, graph the functions. Notice in each case that the numerator and denominator contain at least one com- mon factor. Thus you can simplify each quotient; but don't lose track of the domain of the function as it was initially defined. x + 2 x² - 4 43. (a) y (b) y = (c) y = X + 2 X-2 X-1 (x - 1)(x-2)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_forward
- For Exercises 103–104, given y = f(x), remainder a. Divide the numerator by the denominator to write f(x) in the form f(x) = quotient + divisor b. Use transformations of y 1 to graph the function. 2x + 7 5х + 11 103. f(x) 104. f(x) x + 3 x + 2arrow_forwardWhat is the sign of a if f (x) = ax³ +x +1 satisfies lim f(x) = o0? X -00 %3|arrow_forwardExercise 1: Show that Please show all work and a small explanation. lim x 1 (x 4 1)² = ∞arrow_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_forwardExample 48 lim,(Vx2 + x – Vx² + 5) =?arrow_forward(b) lim (a5+x4)arrow_forward
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