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2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 1 of 8 Current Score : – / 11 Due : Saturday, September 9 2017 11:59 PM MST 1. –/1 pointsSEssCalcET2 2.1.004.

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2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 1 of 8 Current Score : – / 11 Due : Saturday, September 9 2017 11:59 PM MST 1. –/1 pointsSEssCalcET2 2.1.004. Find an equation of the tangent line to the curve at the given point. 2. –/1 pointsSEssCalcET2 2.1.021. If find f'(1) and use it to find an equation of the tangent line to the curve at the point (1, 7). 2.1 Homework (Homework) jarallah almarri MAT 265, section 72204, Fall 2017 Instructor: Sergey Nikitin WebAssign y = x3 − 2x + 2, (3, 23) y = f(x) = 8×2 − x3, y = 8×2 − x3 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 2 of 8 3. –/1 pointsSEssCalcET2 2.1.025. Find f'(a). 4. –/1 pointsSEssCalcET2 2.1.029. Find f(x) = 2×2 − 5x + 1 f'(a) = f'(a). f(x) = 3 − 4x f'(a) = 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 3 of 8 5. –/1 pointsSEssCalcET2 2.1.031. The limit represents the derivative of some function f at some number a. State such an f and a. f(x) = x6 − x, a = 1 f(x) = x7, a = 0 f(x) = x6, a = 1 f(x) = x5, a = 2 f(x) = x6 + x, a = 0 6. –/1 pointsSEssCalcET2 2.1.033. The limit represents the derivative of some function f at some number a. State such an f and a. f(x) = 3x, a = 9 f(x) = 2x, a = 3 f(x) = 3x, a = 2 f(x) = 2x, a = 9 f(x) = x3, a = 2 lim h → 0 (1 + h)6 − 1 h lim x → 2 3x − 9 x − 2 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 4 of 8 7. –/1 pointsSEssCalcET2 2.1.035. The limit represents the derivative of some function f at some number a. State such an f and a. f(x) = cos(x), a = π/4 f(x) = cos(x), a = 0 f(x) = cos(x), a = π/3 f(x) = cos(x), a = π/6 f(x) = cos(x), a = π lim h → 0 cos(π + h) + 1 h 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 5 of 8 8. –/1 pointsSEssCalcET2 2.1.039. The number N of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.) t 1996 1998 2000 2002 2004 2006 N 44 69 109 141 182 233 (a) Find the average rate of cell phone growth between the following years. In each case, include the units. (Round your answers to one decimal place.) (i) from 1998 to 2006 million phones/yr (ii) from 2002 to 2004 million phones/yr (iii) from 2000 to 2002 million phone/yr (b) Estimate the instantaneous rate of growth in 2002 by taking the average of the two average rates of change in (ii) and (iii). What are its units? million phones/yr 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 6 of 8 9. –/1 pointsSEssCalcET2 2.1.043. The cost of producing x ounces of gold from a new gold mine is dollars. (a) What is the meaning of the derivative What are its units? f'(x) is the rate of change of the production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. f'(x) is the total production cost. Its units are dollars. f'(x) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. f'(x) is the total amount of gold produced. Its units are ounces. (b) What does the statement mean? After 800 ounces of gold have been produced, the average production cost is $13/ounce. So the cost of producing 800 ounces is about $13/ounce. The total cost to produce 13 ounces of gold is approximately $800. After 13 ounces of gold have been produced, the average production cost is $800/ounce. So the cost of producing 13 ounces is about $800/ounce. After 800 ounces of gold have been produced, the rate at which the production cost is increasing is $13/ounce. So the cost of producing the 800th (or 801st) ounce is about $13. (c) Do you think the values of will increase or decrease in the short term? What about the long term? Explain. In the short term, the values of will —Select— because more efficient use is made of start-up costs as x increases. But eventually might —Select— due to large-scale operations. C = f(x) f'(x)? f'(800) = 13 f'(x) f'(x) f'(x) 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 7 of 8 10.–/1 pointsSEssCalcET2 2.1.047. The quantity of oxygen that can dissolve in water depends on the temperature of the water. (So thermal pollution influences the oxygen content of water.) The graph shows how oxygen solubility S varies as a function of the water temperature T. (a) What is the meaning of the derivative S ‘(T)? S ‘(T) is the rate at which temperature changes with respect to the temperature. S ‘(T) is the rate at which temperature changes with respect to the oxygen solubility. S ‘(T) is the rate at which oxygen solubility changes with respect to the oxygen solubility. S ‘(T) is the current level of oxygen solubility for a given temperature. S ‘(T) is the rate at which oxygen solubility changes with respect to the water temperature. (b) Estimate the value of S ‘(8). (Round your answer to three decimal places.) S ‘(8) ≈ (mg/L)/°C 2.1 Homework 9/9/17, 4:01 AM https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16578679 Page 8 of 8 11.–/1 pointsSEssCalcET2 2.1.049. Determine whether f ‘(0) exists. f ‘(0) does exist. f ‘(0) does not exist. f(x) = x sin if x ≠ 0 0 if x = 0 4 x

 
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