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Introduction to Calculus

Calculus deals with rates and changes in quantities over time. Calculus is used for many things from calculating how long it takes a projectile to reach the ground after being fired, determining what time in the morning an alarm clock will go off, and even making sure that the temperature outside of your home or work building doesn’t drop below or rise above a certain number. It deals with limits, derivatives, integrals, and infinite sequences. Here, we offer the best Calculus assignment help.

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Calculating Limits

Calculus helps determine when a function will reach a certain number in terms of the value that x takes on when put into functions for f(x). Calculus makes use of limits to help find the rate at which the function is approaching this number. Limits are basically a way of saying that when x approaches some value like a, then f(a) should also approach something close to L.

Calculating Differentiation

Calculus enables students and professionals to determine how fast a function is growing at a certain point. Calculus determines this by taking the derivative of the variable in terms of x over time, or dx/dt. Calculus is used to find important information such as velocity and acceleration rates.

Calculating Integration

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Calculus can also be used to calculate the area between curves. Calculus uses integration to calculate the area under a curve. Calculus uses definite integrals, which are used when calculating finite areas between curves like is done for finding the volume of a solid like a prism given its base and height. Calculus can be used to find the amount of fluid in flexible containers called integral tanks as well.

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Differential calculus involves finding the slope of a tangent at any point on a graph. The calculus helps us determine how fast something is changing based on what it was before and after. The calculus problems are some of the most sought after homework help for high school students as well as college students around the world.

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Differential calculus involves finding an area under a curve on a graph. Differential calculus uses calculus calculus calculus calculus calculus calculus calculus calculus calculus calculus. Differential Calculus helps students find an area under a curve on a graph when given the slope and y-intercept.

Examples of calculus Problems and Solutions

  1. A man is 40 years old today, and the age of his son is seven times his age. If 17 years hence, their ages will be (respectively) 57 and 28, what are their present ages?

Ages for both men today can be represented as x and 7x respectively where x = 40 years. The solution to this problem can be represented as x + 17 = 7x + 57. This can easily be simplified and written as:

Solving for 7x, we get that his age is 9 {since (40+17) / 5 = 57 – 40} years old today.

Half of the sum of two numbers is six. Find the number each of them.

Let x and y be two numbers, x + y = 6. Since we’re given that half of their sum is 6, this can also be written as: (x + y) / 2 =3. This can then be multiplied by 2 giving us: (2x +y)/2 = 6. This can be simplified to: x + y = 3x – 2y {since the left-hand side has been divided by 2 and we’re given that their sum is equal to 6}.

  1. A farmer sold five horses for 1660 pieces of money, and bought three oxen for the same price. He then sold the five horses for 2400 pieces of money and bought two mules. How many mules did he buy?

Let x represent how many horses were sold by the farmer as a total, 5x. By this logic, since he then had 3 oxen left over which cost 1660 coins, we can say that 1660 = x. To solve for x, we can then say that: 5x – 1660 = 0. This can easily be solved to give us 8x = 1660.

We now know that the amount of money he had left over was equal to 8 horses and 1600 / 8 money = 200 pieces of money. Since he sold the number of horses as 5x, he sold them for x / 5 = 200 / 5 pieces of money.

Since the horses were then sold again for 2400 coins and 2 mules were bought, we can say that 2400 + 2 = 2420 pieces of money was spent on the two mules.

We know from solving for x earlier in the problem that 5x = 1660 pieces of money. After the mules were bought we know that 2400 + 2 = 2420 pieces of coins were spent. This means that:

1600 + 2400 – (5x) / 2 x / 5 + 2 = 2420

This can now be simplified to say: x – 3x = -20. This can be used to solve for x by saying that: x = 5x – 3x = 20.

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