1/A/Consider the following.:f(x) = x2 − 4x − 1
Complete the table. (Round your answers to four decimal places.)
| x | 0.9 | 0.99 | 0.999 | 1 | 1.001 | 1.01 | 1.1 |
|
f(x) |
? |
Use the result to estimate the limit. Use a graphing utility to
graph the function to confirm your result. (Round your answer to
four decimal places. If an answer does not exist, enter DNE.)
lim x→1 (x2 − 4x − 1) = ?
Can you please explain in clear details,step by step,how to get those numbers?
B/
C/
Find an equation of the line that is tangent to the graph of fand parallel to the given line. Function Line 2xy 0 f(x) = x2 - 9 y =
Homework Answers
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1/A/Consider the following.:f(x) = x2 − 4x − 1 Complete the table. (Round your answers to four decimal places.) x 0.9...
Complete the table. (Round your answers to four decimal places.)
Complete the table. (Round your answers to four decimal places.) \(\lim _{x \rightarrow 7} \frac{x-7}{x^{2}-8 x+7}\)x6.96.996.99977.0017.017.1f(x)Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.)
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2...
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
hw help Question 1 For the following limit, choose the correct answer. x2 + 4x -...
hw help
Question 1 For the following limit, choose the correct answer. x2 + 4x - 7 lim X 00 e 4x + 6 Does L'Hospitals Rule apply to this problem? If so, why? No. Yes. Indeterminate form olo Yes. Indeterminate form For the following limit, choose the correct answer. x² + 4x - 7 lim e 4x + 6 After applying L'Hospital's Rule once, what will you get? 2x + 4 lim O 4 e4x + 6 x² lim...
Use implicit differentiation to find the following. (Round answers to four decimal places as needed. If...
Use implicit differentiation to find the following. (Round answers to four decimal places as needed. If only th (xy)2 + xy - x = 3,(-3,0) (a) the expression of the slope of the tangent line in terms of x and y dy. -2012 – y + 1 dx2xy + x (b) the equation of the tangent line at the indicated point on the graph y = Use implicit differentiation to find the following. (Round answers to four decimal place In(x...
Use the four-step process to find the slope of the tangent line to the graph of...
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) 8x² + 3x Step 1: f(x + h) = 16x + 24h + 3 X Step 2: f(x + h) - f(x) = n(8h + 2x + 3) X Step 3: f(x + h) - f(x) h 8h + 2x + 3 X Step 4: f'(x) = lim f(x + h) - f(x)...
Consider the following function. f(x) = -½x2 – 3x + 1
Consider the following function. f(x) = -½x2 – 3x + 1 Find the slope and an equation of the tangent line to the graph of the function at the point (-2,5). Slope: m= Equation: y = (Enter equation in slope-intercept form, i.e.y = mx + b)
Consider the function and the value of a. f(x) = -5 X - 1 a =...
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using t...
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
stuck on #37 7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4 5x 35. f) 4x 2 34. f(x)2x 3 36. fx) x2 37. f) 38. f(x) - + 1 In Exercises 39 through 42, first obtai...
stuck on #37
7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4 5x 35. f) 4x 2 34. f(x)2x 3 36. fx) x2 37. f) 38. f(x) - + 1 In Exercises 39 through 42, first obtain the composite functions f(g(x)) and g(f(x)), and then find all number r (if any) such that f(g(x)) g(f(x)). 39. fx) Vt, gt) 1 3
7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4...
Quiz 2 sample 1. Find the derivatives. (a) f(x)-Ssinx+x f(x) (0) f(x) fix-Sx'E f(x) d) fx)...
Quiz 2 sample 1. Find the derivatives. (a) f(x)-Ssinx+x f(x) (0) f(x) fix-Sx'E f(x) d) fx) e f'(x) e) ffx) -sinx cos2x f(x)- 2. Find the equation of the tangent line to yasinx at x-0. 3. Find the points where the tangent line to the function fix)-2x+3x2-12x+4 is horizontal.
Quiz 2 sample 1. Find the derivatives. (a) f(x)-Ssinx+x f(x) (0) f(x) fix-Sx'E f(x) d) fx) e f'(x) e) ffx) -sinx cos2x f(x)- 2. Find the equation of the tangent line...
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
hw help
Question 1 For the following limit, choose the correct answer. x2 + 4x - 7 lim X 00 e 4x + 6 Does L'Hospitals Rule apply to this problem? If so, why? No. Yes. Indeterminate form olo Yes. Indeterminate form For the following limit, choose the correct answer. x² + 4x - 7 lim e 4x + 6 After applying L'Hospital's Rule once, what will you get? 2x + 4 lim O 4 e4x + 6 x² lim...
Use implicit differentiation to find the following. (Round answers to four decimal places as needed. If only th (xy)2 + xy - x = 3,(-3,0) (a) the expression of the slope of the tangent line in terms of x and y dy. -2012 – y + 1 dx2xy + x (b) the equation of the tangent line at the indicated point on the graph y = Use implicit differentiation to find the following. (Round answers to four decimal place In(x...
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) 8x² + 3x Step 1: f(x + h) = 16x + 24h + 3 X Step 2: f(x + h) - f(x) = n(8h + 2x + 3) X Step 3: f(x + h) - f(x) h 8h + 2x + 3 X Step 4: f'(x) = lim f(x + h) - f(x)...
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
stuck on #37
7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4 5x 35. f) 4x 2 34. f(x)2x 3 36. fx) x2 37. f) 38. f(x) - + 1 In Exercises 39 through 42, first obtain the composite functions f(g(x)) and g(f(x)), and then find all number r (if any) such that f(g(x)) g(f(x)). 39. fx) Vt, gt) 1 3
7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4...
Quiz 2 sample 1. Find the derivatives. (a) f(x)-Ssinx+x f(x) (0) f(x) fix-Sx'E f(x) d) fx) e f'(x) e) ffx) -sinx cos2x f(x)- 2. Find the equation of the tangent line to yasinx at x-0. 3. Find the points where the tangent line to the function fix)-2x+3x2-12x+4 is horizontal.
Quiz 2 sample 1. Find the derivatives. (a) f(x)-Ssinx+x f(x) (0) f(x) fix-Sx'E f(x) d) fx) e f'(x) e) ffx) -sinx cos2x f(x)- 2. Find the equation of the tangent line...
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