# What is the Maclaurin series for TANX?

Jul 8, 2019

## What is the Maclaurin series for TANX?

The Maclaurin series expansion is. tanx=f(0)+xf'(0)+x22!

### What is the Taylor series expansion for the tangent function TANX )?

Sequence of Terms The Power Series Expansion for Tangent Function begins: tanx=x+13×3+215×5+17315×7+622835×9+⋯

#### What is the order of a Maclaurin series?

The Maclaurin Series is a Taylor series centered about 0. The Taylor series can be centered around any number a a a and is written as follows: ∑ n = 0 ∞ f ( n ) ( a ) ( x − a ) n n ! = f ( a ) + f ′ ( a ) ( x − a ) + f ′ ′ ( a ) 2 !

What is the Maclaurin series for Sinx?

The Maclaurin series of sin(x) is only the Taylor series of sin(x) at x = 0. If we wish to calculate the Taylor series at any other value of x, we can consider a variety of approaches.

What is the derivative of TANX?

sec2x
The derivative of tan x is sec2x. When the tangent argument is itself a function of x, then we use the chain rule to find the result.

## What is the power series for Arctan?

We know the power series representation of 11−x=∑nxn∀x such that |x|<1 . So 11+x2=(arctan(x))’=∑n(−1)nx2n . So the power series of arctan(x) is ∫∑n(−1)nx2ndx=∑n∫(−1)nx2ndx=∑n(−1)n2n+1x2n+1 . In order to find the radius of convergence of this power series, we evaluate limn→+∞∣∣∣un+1un∣∣∣ .

### What is the difference between Taylor series and Maclaurin series?

The Taylor Series, or Taylor Polynomial, is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. A Maclaurin Polynomial, is a special case of the Taylor Polynomial, that uses zero as our single point.

#### What is the difference between Taylor and Maclaurin series?

How do you prove Taylor’s theorem?

This suggests that we may modify the proof of the mean value theorem, to give a proof of Taylor’s theorem. The proof of the mean-value theorem comes in two parts: first, by subtracting a linear (i.e. degree 1) polynomial, we reduce to the case where f(a) = f(b) = 0.

What is the first derivative of TANX?

The derivative of tan x is sec2x. When the tangent argument is itself a function of x, then we use the chain rule to find the result.

## What is the derivative of Sinx TANX?

Next, take the natural logarithm of both sides and use a property of logarithms to get ln(y)=tan(x)ln(sin(x)) . =1+ln(sin(x))sec2(x) . Multiplying both sides by y=sin(x)tan(x) now gives the final answer to be ddx(sin(x)tan(x))=(1+ln(sin(x))sec2(x))⋅sin(x)tan(x) .

### Is the Maclaurin series tan x a simple process?

Deriving the Maclaurin series for tan x is a very simple process. It is more of an exercise in differentiating using the chain rule to find the derivatives. As you can imagine each order of derivative gets larger which is great fun to work out. The first one is easy because tan 0 = 0. The first derivative of tan x is very simple as you can see.

#### How to find the Maclaurin series of a function?

The easiest way to find Maclaurin series (and Taylor series in general) for complicated functions is to combine series of simpler functions. The Maclaurin series of a function is defined as the expansion of that function at the point . We find this series by taking repeated derivatives of the function in question and applying the formula

Is the Maclaurin series just a Taylor series?

Maclaurin series is just Taylor series about the point so let’s be more robust and learn to calculate a Taylor series. where is the point where you want the most accuracy of your Taylor polynomial. As with many problems computing Taylor Series, the meat is taking derivatives of your function and then plugging in an argument.

How to find the first 4 terms of the Maclaurin series?

Then its says, using that dy/dx ^^^^^ equal to a particular series, find the first 4 terms of inverse tan of x. I’m confused??? What is it asking here?? It says find the 4 first terms of the maclaurin series of the inverse of tan (x).