Look at the graph of f(x) = sin 1/x. is this function periodic? why or why not?

"No, it is not periodic. The function does not repeat on regular intervals."

Step-by-step explanation:

A periodic function repeats itself at regular intervals.

If you look at the graph, it never repeats at regular intervals. It oscillates back and forth and diverges when x grows larger and larger.

If you look at the third answer choice, it makes the most sense.

Third answer choice is right.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.