NOTE: When using interval notation in WeBWorK, remember that: You use 'INF' for oo and '-INF' for . And use 'U' for the union symbol. Enter DNE if an answer does not exist. f(x) = -3 sin a cos a on (-7, 7) a) Find the critical numbers of f. (Separate multiple answers by commas.) b) Determine the intervals on which f is increasing and decreasing. f is increasing on: f is decreasing on: c) Use the First Derivative Test to determine whether each critical point is a relative maximum, minimum, or neither. Relative maxima occur at a = (Separate multiple answers by commas.) Relative minima occur at a = (Separate multiple answers by commas.)

Q: sin sin(x²) evx (1/2-x)uis

A:

Q: lim sin (–3 x z) = z-3

A: To find- the limit.

Q: how sinx derives to cosx

A:

Q: Use algebraic techniques to determine whether the following function is even, odd, or neither. f(x)…

A:

Q: 4. Let X and Y be metric spaces and f : X → Y be continuous. Let SC X. Show: (b) If S is compact,…

A: First, we prove that fS¯⊆f(S)¯. Given that f is continuous and S¯ is compact, we can say f-1Y-f(S)¯…

Q: Simplify the following as a product of trigonometric functions with no powers. Write the functions…

A: Given that, Now simplify the following trigonometric function:

Q: 2. Simplify, without a fractional answer: 2(1 - cos²x) sin³ x(cos²x+ sin² x)

A:

Q: NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for o and '-INF' for -o.…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.