a ball thrown from the IS fround ud fherI secoud is at distance meter the ground, where S= at - b t2.form he di fferential equatiou asSumin f are arbitrarg constant and from %3D Also Fiud its velocity acceleratiion at given, a =5, b = 2

Q: Directions: Find the derivatives using the definition of limits (4-step Rule). Show each step from…

A: Given: y=2x3-3x2

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A:

Q: j. y = 5ln(x²+4)

A:

Q: -. Let f(x) = 3x²(x − 1)². minimum or neither. Als

A: The given function is ; f(x)=3x2(x-1) 7.

Q: Give the VALUE only. No need to include the unit. * Let s, =15r +10r +20 and s3 = 5t + 40f , t 2 0,…

A:

Q: The Range of y = V9- Vã /x is

A: The function y= √(a-x) is valid for all real     x ≤ a and range of this function is [0,√a]

Q: Suppose and investment's value, V, can be tracked with the function v(t) = 932(1.005)120), www. ,…

A: Option D is correct answer. Detailed solution is given below.

Q: 2. A manufacturer wants to design an open box having a square base and a surface area of 104 square…

A:

Q: b. f(x)=7x²e"

A:

Q: Directions: Find the derivatives using the definition of limits (4-step Rule). Show each step from…

A:

Q: 2) Find the derivative of the function. T(r) = ar² +2e" + a². %3D

A: Since the given function is function of 'r'. I am going to differentiate with respect to 'r'.…

Q: A tractor, starting fiom a down the roacl it accelerates at 4mls? for 10 seconds. Then it trauels at…

A: Acceleration, a = 4m/s2Initial velocity, u=0 m/sStarting time,t =10secUsing formula,Distance,…

Q: Q5: - Find dx for the following functions: 1) y = 3x? – 2vx+ 5

A: Apply the differentiation formula to find dydx for the given function. Differentiate the given…

Q: Locate the stationary point of the following functions and determine their character. y= 1/2x^4 -…

A: Please see the below picture for detailed solution.

Q: 2) Find the derivative of the function. T(r) = ar² + 2e" + n². %3D

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Q: Differentiate the function. y = Sint + π Cost

A: To differentiate y=sint+π cost

Q: compute the derivative of the below graph 6. 4- -3 1 0 -2 -4 -6 w. 2.

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Q: Differentiate the function. y = (4x-2)5 (5-x³) 5

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Q: y=C1e³x + C2e¯ 2x + x

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.