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Calculus

The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.

25,068 Questions

What is the limit of x approaching 2 where the sqrt of bracket 6 minus x bracket minus 2 all divided by sqrt of bracket 3 minus x bracket minus 1?

This is a case where we can apply l'Hopital's rule, separately calculating the derivatives of the numerator and denominator, then take the limit using those:

Limx→2 [(6 - x)1/2 - 2] / [(3 - x)1/2 - 1]

= Limx→2 [1/2(6 - x)-1/2 (-1)] / [1/2(3 - x)-1/2 (-1)]

= Limx→2 (3 - x)1/2 / (6 - x)1/2

= 1/2

How do you solve 3j - 13 equals 11 plus 2j?

3j-13=11+2j

3j-13-2j = 11+2j-2

j-13 = 11

j-13 +13 = 11 + 13 = 24

so j = 24

What is the condition to make a curve smooth?

The curve must have a derivative at every point (except its end point).

-2x - 2y equals -12?

or x + y = 6

That cannot be simplified further and to solve for either variable will require another independent eqaution in x and y

9x plus 8 equals 7x plus 22 x equals?

9x+8=7x+22

To solve for x, combine like terms. (Subtract 7x from both sides, and subtract 8 from both sides. This will give you:

2x=14

Divide both sides by 2. The answer is x=7.

What is the equation for y equals -x equals 1?

Either the answer is

the point in the second quadrant, at a distance of one unit from each of the coordinate axes, or

the question is incomplete.

How does sec-squared x equals 1 plus tan-squared x?

Let s = sin x; c = cos x.

By definition,

sec x = 1/cos x = 1/c; and

tan x = (sin x) / (cos x) = s/c.

We know, also, that s2 + c2 = 1.

Then, dividing through by c2, we have,

(s2/c2) + 1 = (1/c2), or

(s/c)2 + 1 = (1/c)2; in other words, we have,

tan2 x + 1 = sec2 x.

What is f x x-5 x plus 3 standard form?

The answer to f x x-5 x plus 3 standard form is -6. This is a math problem.