We know that Differentiation and Integration of e^x is e^x. Doesn't it mean that the gradient and area covered under the graph of y = e^x is same. If so it is, then how?

Yeah man, the area covered by e^x from 0 to A is e^A, and that value is exactly the gradient in that point, you can prove it by solving the limit h->0 of [f(x+h)-f(x)]/h, which describes the gradient of the graph in each point

The derivative is the slope of the tangent. i.e. the slope of the curve at a particular point. The gradient is the normal to the curve at the point of tangency and is therefore perp to the tangent. So the answer is no. At (a,e^a) the slope of the tangent is e^a. Therefore the slope of the gradient is -1/e^a

The area under e^x from -inf to A is e^a -- as stated by Phinehas.

The slope of the tangent to e^x at x = A is e^A

"Yeah man, the area covered by e^x from 0 to A is e^A"

No. The area under the curve e^x from 0 to A is (e^A - 1).

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Differentiation is a method to find the gradient of the curve.

Integration is a method to find the area under the curve from (minus infinity) to x.

Yeah man, the area covered by e^x from 0 to A is e^A, and that value is exactly the gradient in that point, you can prove it by solving the limit h->0 of [f(x+h)-f(x)]/h, which describes the gradient of the graph in each point

You mean negative infinity to A

The derivative is the slope of the tangent. i.e. the slope of the curve at a particular point. The gradient is the normal to the curve at the point of tangency and is therefore perp to the tangent. So the answer is no. At (a,e^a) the slope of the tangent is e^a. Therefore the slope of the gradient is -1/e^a

The area under e^x from -inf to A

is e^a-- as stated by Phinehas.The slope of the tangent to e^x at x = A

is e^A"Yeah man, the area covered by e^x from 0 to A is e^A"No. The area under the curve e^x from 0 to A is (e^A - 1).

I will always let you and your words become part of my day because you never know how much you make my day happier and more complete. There are even times when I feel so down but

write my assignment for meI will feel better right after checking your blogs. You have made me feel so good about myself all the time and please know that I do appreciate everything that you haveStunning site! Do you have any accommodating clues for trying essayists? I’m wanting to begin my own site soon yet I’m somewhat lost on everything. Would you prompt beginning

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