One can use integration by parts to solve this. The answer is (x-1)e^x.
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.
The integral would be 10e(1/10)x+c
A graph is a function if there is no more than one y-value for any x value. This means no vertical lines or "C" shapes, etc
No.The equation x/(x^2 + 1) does not have a vertical asymptote.
There are two main definitions. One defines the integral of a function as an "antiderivative", that is, the opposite of the derivative of a function. The other definition refers to an integral of a function as being the area under the curve for that function.
No. If an input in a function had more than one output, that would be a mapping, but not a function.
No. If the function has more than one x-intercept then there are more than one values of x for which y = 0. This means that, for the inverse function, y = 0 should be mapped onto more than one x values. That is, the inverse function would be many-to-one. But a function cannot be many-to-one. So the "inverse" is not a function. And tat means the original function is not invertible.
I assume you mean -10x^4? In that case, antiderivative would be to add one to the exponent, then divide by the exponent. So -10x^5, then divide by 5. So the antiderivative is -2x^5.
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
yes
No. One argument of function may have only one value. So, if it has more than one value, it is not a function.
No. A function has only one output per input.
1) First you get the anti-derivative of sin z. This one is easy; you can look it up in the most basic standard tables of integrals. 2) Use the fundamental theorem of calculus: a. Calculate the antiderivative function for the upper limit. b. Calculate the antiderivative function for the lower limit. c. Subtract the answer of part "a" minus the answer of part "b".
No, it does not.
No. In fact, a function can't have an answer at all, because it's not a question.An equation has an answer, and possibly more than one.In general, an equation is in the form of (one function) = (another function).(One of the functions may be zero or a constant.)
No, it is not. A function can only have one output per input. (If it has more than one, it is still maths, but it cannot be called a "function". It would probably be called an equation or a formula etc...).