do number 6 pls and pls show all the work (1) Find the antiderivative of f(x). Initial condition is f(0) =3. Let f'(x) = 4x³ + x² – 3x(2) Find the function g(x) where g'(x) = 4 sin x + 7* - 5(3) Find y' and then evaluate it for (-2,3)e2x-1(4) Find the limit:lim-x-0 cos x-13x³ + y² = -xy(5) Find absolute maximum and absolute minimum off(x) = x³ 3x² + 1 with the domain of [-2, 4](6) Compute Vy and dy for f(x) = x - x³ where x = 1 and Vx = 0.1(7) Air is being pumped into a spherical balloon so that the volume increases at a rate of 50cubic feet per second. How fast is the radius of the balloon increased when thediameter is 26 feet.Diameter 2 times radius.Circle Area = Circle Area = nr²Sphere Volume.v=r³(8) Find the limit. Must use l'Hospital Rule. limIn xx-xx-1Find the derivative:(9) Find the equation of the tangent line to y = 2t sint at point (₁)(10)cost1-sin tet (t³).Evaluate the drivative for t = 0

Using derivatives we can solve the question.Note : I am authoring Question 6 as asked.

Answered: (6) Compute Vy and dy for f(x) = x - x³…

Math

Calculus

(6) Compute Vy and dy for f(x) = x - x³ where x = 1 and Vx = 0.1

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

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Question

do number 6 pls and pls show all the work

(1) Find the antiderivative of f(x). Initial condition is f(0) =3. Let f'(x) = 4x³ + x² – 3x
(2) Find the function g(x) where g'(x) = 4 sin x + 7* - 5
(3) Find y' and then evaluate it for (-2,3)
e2x-1
(4) Find the limit:
lim-
x-0 cos x-1
3x³ + y² = -xy
(5) Find absolute maximum and absolute minimum of
f(x) = x³ 3x² + 1 with the domain of [-2, 4]
(6) Compute Vy and dy for f(x) = x - x³ where x = 1 and Vx = 0.1
(7) Air is being pumped into a spherical balloon so that the volume increases at a rate of 50
cubic feet per second. How fast is the radius of the balloon increased when the
diameter is 26 feet.
Diameter 2 times radius.
Circle Area = Circle Area = nr²
Sphere Volume.
v=r³
(8) Find the limit. Must use l'Hospital Rule. lim
In x
x-xx-1
Find the derivative:
(9) Find the equation of the tangent line to y = 2t sint at point (₁)
(10)
cost
1-sin t
et (t³).
Evaluate the drivative for t = 0

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