Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function s = f( t) = 5 t 2+ 17 t. Calculate the (instantaneous) velocity of the car when t= 27. a. 22 ft/sec b. 287 ft/sec c. 4104 ft/sec d. 594 ft/sec

Q: Find the derivative of the function. t3 2 h(t) : to + 3 h'(t) =

A: Given function: Used formulas: Chain rule of differentiation, Quotient rule of differentiation,…

Q: The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t…

A: We can find the instantaneous velocity as below

Q: If a ball is thrown into the air with a velocity of 34 ft/s, its height (in feet) after t seconds is…

A:

Q: On her bicycle ride Fabiana's position (in km) as a function of time (in hours) is s(t) = 22t + 17.…

A: Fabiana’s position (in km) as a function of time (in hours) is given by

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A: The displacement is given by

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A: For the average velocity first, find the displacement between t=1 and t=3 seconds and then divide it…

Q: Find the derivative of the function. f(t) =   1/2 (8t2 + t)−3

A: d/dt(f(t)^n) = nf(t)^(n-1)(d/dt (f(t))

Q: On her bicycle ride Fabiana's position (in km) as a function of time (in hours) is s(t)=13t+17. a.)…

A:

Q: The driver of a car traveling at 48 ft/sec suddenly applies the brakes. The position function of the…

A: Topic- application of derivatives

Q: Find the derivative of the function.

A: ddx3x2+4x-8x32Apply the Quotient Rule:  fg'=f '·g-g'·fg2=ddx3x2+4x-8x32-ddxx323x2+4x-8x322Solving,…

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A:

Q: For the function f (t) = 3t4 – t, the average rate of change in f from t = -1 to t = 3 is %3D…

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Q: Suppose the height of a rocket rising vertically from the ground is modelled by the equation; S(t)=…

A: Here equation is S(t)=t2+2t+4A)we have S(t)=t2+2t+4put t=1 and t=8 in…

Q: The derivative dy for the function y=($ +5> 515

A: Here we will use power rule to differentiate

Q: In the given eqaution/s, find the derivative of the function:-   f (t)= (9t + 2)2 /3

A: Consider the given function. ft=9t+223 The chain rule is defined as. dfgtdt=ddtfgtddtgt

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A:

Q: Solve for the derivative of the following function: v=1/t^3

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Q: find derivative of the function  h(t) = t2(8t + 7)3

A:

Q: Find the derivative of the function. Re) = (6t + 17)2/3 f '(t) =

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Q: Find the derivative of the function .

A: The given function is  ft=t23-t13+4

Q: Find the derivative of the function. s(t) = 43 (9t° - 7) s'(t) =| 514

A: S'(t)=?

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A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A: We will find f'(x) using the product rule and the chain rule.

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A: To find the instantaneous velocity at t=1.5 seconds

Q: Find the second derivative of the function.

A: The given function: g(t)=-8t3-5t+12

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Q: Suppose the distance s (in feet) traveled by a car moving along a road after t seconds is given by…

A:

Q: Find the derivative of the function. 4 e W 7w dr dw %3D

A: We have to find the derivative of the given function

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Q: Find the derivative of the function. h(t)=(t^3/t^8+5)^2

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A:

Q: Suppose the distance "s" (in feet) covered by a car moving along a straight road after "t" sec is…

A: The objective of the question is determine the velocity when t=27.

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Q: Find the derivative of the following function. 6. m(t) = – 2t (3t“ – 1) " m'(t) =

A:

Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted

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A: Use instantaneous velocity concept

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A: topic - average value of function

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A:

Q: Q3/ find the derivative La)= メ 2. logs (x+3) 2x+4

A:

Q: Find the derivative of the function w=(9r−4)^4. dw/dr=?

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Q: Let s(t) = t2+2 be the position of a car on a road, where s(t) is in feet and t is in seconds.  Find…

A: Given,

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A: Here we have  S(t)= 3-4t At t=8

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A:

Q: The velocity, v of a body as a function of time, t is given as v(t) = 5e4+4, where t is in seconds,…

A: Since, we have been given that v(t)=5e-2t+4-(i), where t is in secondsand v is in m/s.Our Aim is to…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.