yes, look at the function f(x)=3x^2 The antiderivative is x^3+C where C is the constant and is more than one value for C. In fact, 3x^2 will have an infinite number of antiderivatives.
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.
yes
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.
No. A function has only one output per input.
No. One argument of function may have only one value. So, if it has more than one value, it is not a function.
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...).
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".