1. Explain why the graphs of tangent and cotangent have vertical
asymptotes
2. Explain why the graphs of cosecant and secant have vertical
asymptotes
3. Sketch a graph of y=3sec(2x)y=3sec(2x) by hand, in other
words, without a graphing utility. Include 2 periods, and include
the asymptotes.
Analyticity of trigonometric functions (a) Directly from the
definition, construct the Taylor Series centered at x = 0 for the
function f(x) = cos(x). (b) Show that this series converges for all
x ∈ R. (c) Show that this series converges to cos(x) for all x ∈
R.
for loop practice – Taylor Series!The moment you finish
implementing the trigonometric functions, you realize that you have
forgotten your favorite function: the exponential! The Taylor
Series for the exponential function is
푒푥=1+푥1!+푥22!+푥33!+...,‒∞<푥<∞a) Using a for loop, compute and
display the error of the Taylor series when using 12 and 15 terms,
each as compared to the exponential function when evaluated at x =
2. b) Can you figure out how to compute and display the number of
terms necessary...
Utilize identities to calculate the exact value of the five
remaining trigonometric functions if:
csc(α)= √3, π/2, < α < π
Calculate the equivalent algebraic expression for:
sec(arcsin(x - 1)
1. Is it possible for a rational function to have no vertical
asymptotes? If yes the how? If no then why?
2. What is the fundamental difference between a rational
function and a polynomial function?
3. Can a rational function have no x - intercepts? If so then
how?
4. Can a rational function have two y-intercepts? Why or why
not?
5. Can the graph of a rational function cross the vertical
asymptote? Why or why not?
Please TYPE out...
f(x)=e^x/(x+1)
Find the vertical and horizontal asymptotes using limits. Also,
intervals of increase and decrease, local extrema. Finally, find
the intervals of concavity and points of inflection.