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ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y=...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
Using the definition, calculate the derivative of the function. Then find the values of the derivative...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative...
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x – 1)+8x²(2x – 1)+ 16x(x? + 1) and third derivative is f"(x) = 24x(2x – 1) +24(x + 1) +48x2. True False dy Given the equation x3 + 3 xy + y2 = 4. We find dx 2 x' + y by implicit differentiation and is to be y' = x + y2 True False Let f(x)= x...
as a function of x. Nrite the function below in the form y = f(u) and...
as a function of x. Nrite the function below in the form y = f(u) and u = g(x). Then find dy dx y = √5x² - 6x +5 Write the function in the form y=f(u) and u = g(x). Choose the correct answer below. OA. y = Vu and u = 5x2 - 6x + 5 OB. y=u and u =5x2 - 5x+5 OC. y = 5u? - 5u +5 and u = x OD. y = 5u2 -...
3. (a) Let f be an infinitely differentiable function on R and define х F(x) =...
3. (a) Let f be an infinitely differentiable function on R and define х F(x) = e-y f(y) dy. Find and prove a formula for F(n), the nth derivative of F. (b) Show that if f is a polynomial then there exists a constant C such that F(n)(x) = Cem for sufficiently large n. Find the least n for which it is true.
11. a) Find the derivative of f(x) by using the definition of derivative: lim f(x+4x) -...
11. a) Find the derivative of f(x) by using the definition of derivative: lim f(x+4x) - f (x ) Ax0 Ar f(x) = 4x² +8 Make sure you show all your work clearly and neatly!!! If steps are not clearly written you will not receive any credit. (9 points) f'(x) = b) Check your answer from part (a) by finding the derivative of f(x) = 4x² +8. (1 pts) f'(x)= c) What is the instantaneous rate of change of the...
find the derivative Find the derivative of the function. y=9 eX + e 2x dy dx...
find the derivative
Find the derivative of the function. y=9 eX + e 2x dy dx
Find the derivative of the function. y=9 eX + e 2x dy dx
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x)...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
3. (a) (3 points) Write the definition of the derivative of a differentiable function f(x) at...
3. (a) (3 points) Write the definition of the derivative of a differentiable function f(x) at = a; (b) (7 points) using the definition of derivative as in (a), find the derivative of the function f(x) = Vx at a = 2. (c) EXTRA CREDIT (2 points): State the MEAN VALUE THEOREM (you can also draw a picture) and give its PHYSICAL interpretation in terms of INSTANTANEOUS and AV- ERAGE VELOCITIES.
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values...
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values of f' are given in the table above. It is known that f(0) = 3. (a) For f'(x), the conditions of the Mean Value Theorem are met on the closed interval (0,3). The conclusion of the Mean Value Theorem over the interval (0,3) for f'(x) is satisfied at c = 1. Find f"(c). (b) Use a right Riemann sum with the three subintervals indicated...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x – 1)+8x²(2x – 1)+ 16x(x? + 1) and third derivative is f"(x) = 24x(2x – 1) +24(x + 1) +48x2. True False dy Given the equation x3 + 3 xy + y2 = 4. We find dx 2 x' + y by implicit differentiation and is to be y' = x + y2 True False Let f(x)= x...
as a function of x. Nrite the function below in the form y = f(u) and u = g(x). Then find dy dx y = √5x² - 6x +5 Write the function in the form y=f(u) and u = g(x). Choose the correct answer below. OA. y = Vu and u = 5x2 - 6x + 5 OB. y=u and u =5x2 - 5x+5 OC. y = 5u? - 5u +5 and u = x OD. y = 5u2 -...
3. (a) Let f be an infinitely differentiable function on R and define х F(x) = e-y f(y) dy. Find and prove a formula for F(n), the nth derivative of F. (b) Show that if f is a polynomial then there exists a constant C such that F(n)(x) = Cem for sufficiently large n. Find the least n for which it is true.
11. a) Find the derivative of f(x) by using the definition of derivative: lim f(x+4x) - f (x ) Ax0 Ar f(x) = 4x² +8 Make sure you show all your work clearly and neatly!!! If steps are not clearly written you will not receive any credit. (9 points) f'(x) = b) Check your answer from part (a) by finding the derivative of f(x) = 4x² +8. (1 pts) f'(x)= c) What is the instantaneous rate of change of the...
find the derivative
Find the derivative of the function. y=9 eX + e 2x dy dx
Find the derivative of the function. y=9 eX + e 2x dy dx
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
3. (a) (3 points) Write the definition of the derivative of a differentiable function f(x) at = a; (b) (7 points) using the definition of derivative as in (a), find the derivative of the function f(x) = Vx at a = 2. (c) EXTRA CREDIT (2 points): State the MEAN VALUE THEOREM (you can also draw a picture) and give its PHYSICAL interpretation in terms of INSTANTANEOUS and AV- ERAGE VELOCITIES.
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values of f' are given in the table above. It is known that f(0) = 3. (a) For f'(x), the conditions of the Mean Value Theorem are met on the closed interval (0,3). The conclusion of the Mean Value Theorem over the interval (0,3) for f'(x) is satisfied at c = 1. Find f"(c). (b) Use a right Riemann sum with the three subintervals indicated...
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