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Dec 30, 2015 · We used the theorem that states that if a sequence converges, then every subsequence converges to the same limit. By modus tollens, our sequence does not converge. More info about the theorem here: Prove: If a sequence converges, then every subsequence converges to the same limit.

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities solves extremely difficult trigonometric problems. Conversions of Angles converts radian to degree scale.

In fact, sin(1/x) wobbles between -1 and 1 an infinite number of times between 0 and any positive x value, no matter how small. To see this, consider that sin(x) is equal to zero at every multiple of pi, and it wobbles between 0 and 1 or -1 between each multiple.

Oct 3, 2009 · The limit — informally — is the single number (y-value) that a function is approaching as the x-value is getting closer and closer to 0. But as x gets closer and closer to 0, the y value [sin(1/x)] bounces between 1 and -1 more and more frequently.

To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for the variable. Use inverse trigonometric functions to find the …

We take the functions $g(x)=\frac{1}{x}$ and $h(x)=\sin(x)$, now we see that: $g(x)$ is continuous in the open interval $(-\infty,0) \cup (0,\infty)$ because it's defined for every $x \in R$ except in $x=0$.

What is the general solution for sin (x)=1 ?

Instead of looking at $\frac{\sin(1/x)}{1/x}$ for small $x$, you can look at $\frac{\sin(y)}{y}$ for large $y$. Now things should be more obvious: the denominator gets large, while the absolute value of the numerator stays less then or equal to $1$. Hence, the fraction will tend to $0$.