# 50+ Calculus Questions and Answers

Q: how to find dot product?

A: If a and b are vectors, then the dot product is a*b=ab=axbx+ayby+azbz

Q: how to solve an exponential equation?

A: There is no one-size-fits-all answer to this question, as the method for solving an exponential equation will vary depending on the equation in question. However, some common methods for solving exponential equations include using properties of exponents, taking logarithms, and using inverse functions.

Q: how to evaluate integrals?

A: There are a few different ways to evaluate integrals, depending on the function being integrated. The most common method is to use integration by substitution, which involves finding a new function that is easier to integrate. Another common method is to use integration by parts, which involves breaking up the function into simpler pieces. There are also a few numerical methods that can be used to approximate the value of an integral.

Q: what is the derivative of x?

A: X is not a function, so it does not have a derivative.

Q: how to synthetic division?

A: Synthetic division is a method for dividing polynomials that is quicker and easier than standard polynomial division.

Q: what is the integral of e^x?

A: The integral of e^x is e^x.

Q: what is the derivative of cos x?

A: The derivative of cos x is -sin x.

Q: what is the derivative of sin?

A: y=sinx

Q: how to solve for x in logs?

A: The equation is not solvable as written.

Q: how to take antiderivative?

A: The integral of a function is the antiderivative of the function.

Q: what is the derivative?

A: The derivative is the slope of the function at a given point.

Q: how to find partial derivatives?

A: If you have a function represented by a formula, you can take the derivative of that function by using the rules of calculus. For example, if you have a function f(x) = x^2, then the derivative of that function with respect to x would be f’(x) = 2x.

Q: what is a line integral?

A: a mathematical process for determining the quantity which is the product of a function and the length of a curve.

Q: what is the derivative of e?

A: The derivative of e is e.

Q: what is f’(x)?

A: f’(x) is the rate of change of f(x).

Q: what is identity function?

A: A function that always returns the same output for the same input.

Q: what is the derivative of e^-x?

A: The derivative of e^-x is -e^-x

Q: what is odd integers?

A: Odd integers are whole numbers that cannot be divided evenly by 2.

Q: how to use the substitution method?

A: If you are trying to solve a system of linear equations, the substitution method is when you isolate one variable in one equation, and then plug that result into the other equation. This will give you a new equation with one variable that you can solve.

Q: how to write an exponential function from a table?

A: I would plot the points on a graph and then use the points to find a trend. From there, I would use that trend to write an exponential function.

Q: what is antiderivative?

A: At its simplest, an antiderivative is a function that is the “inverse” of the derivative operation. So, if you have a function f(x) that is the derivative of another function g(x), then g(x) is an antiderivative of f(x).

Q: how to take the derivative of e?

A: One way to take the derivative of e is to use the power rule of calculus. This states that the derivative of a function raised to a power is equal to the product of the exponent and the function raised to the power minus one. Therefore, the derivative of e raised to a power x would be xe raised to the power x-1. Another way to take the derivative of e is to use the natural logarithm. This states that the derivative of e raised to a power x is equal to the natural logarithm of e multiplied by e raised to the power x.

Q: how to find the interval of convergence?

A: $$\displaystyle \cos \left( \frac12 \pi n \right) \sum_{n=0}^{\infty} a_n x^n=0.$$

Q: how to evaluate log expressions?

A: The first step is to rewrite the expression in exponential form. Then, use a calculator to compute the value of the exponential expression.

Q: how to find the zeros of a function on a graph?

A: Zeros are points where the graph of the function intersects the x-axis.

Q: how to find indefinite integral?

A: The indefinite integral of a function is the antiderivative of the function.

Q: what is the integral of 0?

A: The integral of 0 is 0.

A: To find adjacent elements in an array, you can use the indexOf() method to find the position of one element, and then use the slice() method to get the elements before and after it.

Q: what is the integral of 1 x?

A: ∫1x = x

Q: what is the integral of zero?

A: The integral of zero is zero.

Q: what is the antiderivative of cos?

A: the antiderivative of cos is sin

Q: what’s the derivative of tangent?

A: the derivative of tangent is secant squared

Q: what does array means in math?

A: In mathematics, an array is a data structure that allows you to store a sequence of elements.

Q: what is the integral of e^2x?

A: e^{2x}

Q: what is the integral of x?

A: the integral of x is x*dx

Q: what is a logarithmic equation?

A: A logarithmic equation is an equation in which the unknown quantity is the logarithm of another quantity.

Q: how to find slope of a tangent line?

A: To find the slope of a tangent line, we need to take the derivative of the function at that point.

Q: how many values are in the range 35 to 95?

A: there are 60 values in the range 35 to 95

Q: how to find derivative of ln?

A: For finding the derivative of ln, we can use the definition of derivative.

Q: how to find derivatives?

A: There is no general rule for finding derivatives, as the process depends on the function being differentiated.

Q: how to calculate riemann sum?

A: Riemann sum is calculated by dividing the interval into subintervals, selecting the endpoint of each subinterval, and multiplying each endpoint by the corresponding function value. The sum of the products is the Riemann sum.

Q: how to find limit of a function?

A: There are a few different methods that can be used to find the limit of a function at a certain value. One method is to plug the value into the function and see what happens. Another method is to take the limit of the function as the input values approach the value from either side.

Q: how to solve for limits?

A: The limit of a function is the value that the function approaches as the input values get closer and closer to some value. The limit of a function at some value can be found by taking the limit of the function as the input values approach that value from either side.

Q: what is a leading coefficient in a polynomial?

A: A leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Q: what is the derivative of absolute value of x?

A: \$\frac{d}{dx}\lvert x\rvert = \begin{cases}

Q: what does the first derivative tell you?

A: The first derivative tells you the slope of the graph at any given point.

Q: what is the derivative of sine?

A: The derivative of sine is cosine.

Q: how many subsets with an odd number of elements does a set with 10 elements have?

A: 4,096

Q: how many ways are there to distribute six indistinguishable balls into nine distinguishable bins?

A: ?

A: There are 926 possible ways.

Q: in how many different orders can five runners finish a race if no ties are allowed?

A: ?

A: in how many different orders can five runners finish a race if no ties are allowed?

A: ?

A: A: If no ties are allowed, then the five runners can finish in any order. Thus, there are 5! = 120 different orders in which the runners can finish.

Q: how to find derivative of e?

A: The derivative of e is e.

Q: how many solutions does?

A: not a math question

Q: how to tell if a graph is exponential?

A: If a graph is exponential, it will have a curved shape and will increase or decrease at a constant rate.

Q: how to find the derivative of e^x?

A: The derivative of e^x is e^x.

Q: how to use linear approximation?

A: To find a linear approximation of a function, you need to find the equation of the line that best approximates the function near a given point. To do this, you need to find the slope of the function at that point and use the point-slope form of the equation of a line.

Q: how to find exponential equation from graph?

A: If you have a graph of an exponential function, you can find the equation by taking the natural log of both sides.

Q: how to find the derivative of an exponential function?

A: The derivative of an exponential function is the exponent times the original function.

Q: how to find the derivative of an equation?

A: Take the derivative of both sides of the equation with respect to the variable you are differentiating.