What type of function is Xsinx?

Even functions are symmetrical about the y-axis. Odd functions have symmetry about the origin. thus xsinx is an even function. This is graph of xsinx.

Is Xsinx uniformly continuous?

To show that x sin x is not uniformly continuous, we use the third criterion for nonuniform continuity. +yn sin yn)=4π2. In particular, there exists a K such that for n ≥ K, |xn sin(xn) − un sin(un)| > 1. So x sin x is not uniformly continuous.

Is Tan Xa continuous function?

Originally Answered: Is tan(x) a continous function? No it is not a continuous function. That is because when x=positive or negative[ (2n-1)*(pie/2) ], then the range of the function tanx becomes infinity. So there is a discontinuity at these points.

Are logs continuous?

Definition: Continuity A function f is continuous if it is continuous at every point in its domain. For instance, the natural logarithm ln(x) is only defined for x > 0. This means that the natural logarithm cannot be continuous if its domain is the real numbers, because it is not defined for all real numbers.

Is Xcosx even or odd?

Since −xcos(x)=−xcos(x) – x cos ( x ) = – x cos ( x ) , the function is odd.

Is FX COSX odd or even?

cos(x)=cos(−x) , therefore cosine is an even function.

Is Lnx continuous?

The function lnx is differentiable and continuous on its domain (0,с), and its derivative is d dx lnx = 1 x . function is continuous, therefore lnx is continuous.

How do you show something is not uniformly continuous?

If f is not uniformly continuous, then there exists ϵ0 > 0 such that for every δ > 0 there are points x, y ∈ A with |x − y| < δ and |f(x) − f(y)| ≥ ϵ0. Choosing xn,yn ∈ A to be any such points for δ = 1/n, we get the required sequences.

Is tan 2x continuous?

Therefore,tan(2x) is continuous everywhere except at x,where x=\frac{n \pi}{4},where n odd numbers.

Where are logarithmic functions continuous?

Theorem 8.1 log x is defined for all x > 0. It is everywhere differentiable, hence continuous, and is a 1-1 function. The Range of log x is (−∞, ∞).

Is Xcosx an even function?

Since −xcos(x) – x cos ( x ) ≠ ≠ xcos(x) x cos ( x ) , the function is not even.

Is 2cosx even or odd?

Precalculus Examples A function is even if f(−x)=f(x) f ( – x ) = f ( x ) . Check if f(−x)=f(x) f ( – x ) = f ( x ) . Since 2cos(x)=2cos(x) 2 cos ( x ) = 2 cos ( x ) , the function is even.