Graph of sinhx^-1 | What is sinh^-1x graph drawing?

The graph of sinhx to the -1 is as follows.

$sinhx^{-1}$ graph:

sinh^-1x graph

Read More

Special Power Series | ex | sinx | cosx | tanx | ln(1+x) | sinhx | coshx | tanhx | sinh^-1 | tanh^-1 All Series

You can reach all special power series formulas from below. We wish you all good lessons...

$e^x$ series:

(all x)

sinx series:

(all x)

cosx series:

(all x)

tanx series:

(|x| < π/2)

$sin^{-1}x$ series:

(|x|<1)

$tan^{-1}x$ series:

(|x|<1)

ln(1+x) series:

(-1<x≤1)

sinhx series:

(all x)

coshx series:

(all x)

tanhx series:

(|x|<π/2)

$sinh^{-1}x$ series:

(|x|<1)

$tanh^{-1}x$ series:

(|x|<1)

Read More

Maclaurin Series Formula | What is the Maclaurin series?

If the series is zero-centered (a=0), the Taylor series takes a simpler form and this special series is called the Maclaurin series after the Scottish mathematician Colin Maclaurin.

Maclaurin Series Formula:

Read More

Epicycloid Definition | Epicycloid Parametric Equations

 

Parametric equations:

This is the curve described by a point P on a circle of radius b as it rolls on the outside of a circle of radius a. The cardioid is a special case of an epicycloid.

Read More

Z Transforms | All Function and Transform

You can find all the Z transforms below. We wish you good work...

Shift Theorem

Initial value theorem

Final value theorem

provided f(∞) exists.

Inverse Formula

Read More

Mechanics Kinematics & Centres of Mass Definitions and Formulas

Kinematics:

Motion constant acceleration

$v=u+ft$

$s=ut+\frac{1}{2}ft^2=\frac{1}{2}(u+v)t$

$v^2=u^2+2f.s$

General solution of $\frac{d^2x}{dt^2}=-w^2x$ is

x=a.coswt + b.sinwt = R.sin(wt+φ)

where $R=\sqrt{a^2+b^2}$ and cosφ = a / R, sinφ = b / R.

In polar coordinates the celocity is  and the acceleration is

Centres of mass:

The following results are for uniform bodies:

• hemispherical shell, radius r    ⇾    $\frac{1}{2}r$                    ⇾     from centre
• hemisphere, radius r                 ⇾    $\frac{3}{8}r$                  ⇾     from centre
• right circular cone, height h      ⇾    $\frac{3}{4}h$                  ⇾     from vertex
• arc, radius r and angle 2θ         ⇾    (r sinθ) / θ       ⇾     from centre
• sector, radius r and angle 2θ    ⇾    ($\frac{2}{3}r$ sinθ) / θ    ⇾     from centre

Read More

Chebyshev Polynomials

You can find the Chebyshev polynomials below. We wish everyone a good lesson...

Read More