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f(-1+h)-f(-1) for Let fæ) = V2 +5. Calculate the difference quotient h= .1 h = .01...
Thank you. - Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate...
Thank you.
- Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). Suppose (2) = - 2 (7+h)-(7) 1-10) lim A0 (0)-0 0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the slope of the tangent line to the...
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x)...
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x) = lim h0 (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ar because it is easier to type) We can cancel the common factor — from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = 6. (10 points) Let f(x) = x3...
Let f(x) = 2 + 5x2 – 2x3. (a) Find the slope m of the tangent...
Let f(x) = 2 + 5x2 – 2x3. (a) Find the slope m of the tangent line to the graph off at the point where x = a. ma (b) Find an equation of the tangent line to the graph off at the point (1, 5). y(x) = (c) Find an equation of the tangent line to the graph off at the point (2,6). y(x) = (d) Use technology to graph fand the two tangent lines in the same viewing...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line with positive slope that is tangent to both of the parabolas y = f(x) and y = g(x) simultaneously. ye9bx)/ y=f/ Find the equation of the line. y= On a separate piece of paper, sketch the graph of the parabola y = 2? + 6. On the same graph, plot the point(0, – 3). Note that there are two tangent lines of y =...
Calculate the difference quotients for f(x) = 9 - 4x using h = 0.1, 0.01 and...
Calculate the difference quotients for f(x) = 9 - 4x using h = 0.1, 0.01 and 0.001. Use the results to approximate the slope of the tangent line to the graph off(x) at the point (6. - 15). If necessary, round the difference quotients to no less than six decimal places and round your final answer to two decimal places Calculate the difference quotients for f(x) = 4 + 3x usingh 0.1 0.01, and 0.001. Use the results to approximate...
Math 141 Homework 2 June 21, 2019 Problem 1 Use the difference quotient to determine f'(x)...
Math 141 Homework 2 June 21, 2019 Problem 1 Use the difference quotient to determine f'(x) for a. f(r)r2 c. f(x) = -2r Problem 2 Find and simplify the difference quotient for f(x)= r2- 4r Problem 3 Find the slope of the line tangent to f(x) = -312 - 4r +2 at (2,-3). 1
Math 141 Homework 2 June 21, 2019 Problem 1 Use the difference quotient to determine f'(x) for a. f(r)r2 c. f(x) = -2r Problem 2 Find...
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...
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...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) -...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Thank you.
- Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). Suppose (2) = - 2 (7+h)-(7) 1-10) lim A0 (0)-0 0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the slope of the tangent line to the...
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x) = lim h0 (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ar because it is easier to type) We can cancel the common factor — from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = 6. (10 points) Let f(x) = x3...
Let f(x) = 2 + 5x2 – 2x3. (a) Find the slope m of the tangent line to the graph off at the point where x = a. ma (b) Find an equation of the tangent line to the graph off at the point (1, 5). y(x) = (c) Find an equation of the tangent line to the graph off at the point (2,6). y(x) = (d) Use technology to graph fand the two tangent lines in the same viewing...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line with positive slope that is tangent to both of the parabolas y = f(x) and y = g(x) simultaneously. ye9bx)/ y=f/ Find the equation of the line. y= On a separate piece of paper, sketch the graph of the parabola y = 2? + 6. On the same graph, plot the point(0, – 3). Note that there are two tangent lines of y =...
Calculate the difference quotients for f(x) = 9 - 4x using h = 0.1, 0.01 and 0.001. Use the results to approximate the slope of the tangent line to the graph off(x) at the point (6. - 15). If necessary, round the difference quotients to no less than six decimal places and round your final answer to two decimal places Calculate the difference quotients for f(x) = 4 + 3x usingh 0.1 0.01, and 0.001. Use the results to approximate...
Math 141 Homework 2 June 21, 2019 Problem 1 Use the difference quotient to determine f'(x) for a. f(r)r2 c. f(x) = -2r Problem 2 Find and simplify the difference quotient for f(x)= r2- 4r Problem 3 Find the slope of the line tangent to f(x) = -312 - 4r +2 at (2,-3). 1
Math 141 Homework 2 June 21, 2019 Problem 1 Use the difference quotient to determine f'(x) for a. f(r)r2 c. f(x) = -2r Problem 2 Find...
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...
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...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
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