Question

use
the squeeze theorum to show that

*** please show work

limx→0 cos(x)x^8 sin(1/x)=0

limx→0 tan(x)x^4 cos(2/x)=0

Answer #1

Evaluate each of the following limits. a) limx→∞(x/x − 2)^x
b) limx→0 sin x cos x/x + tan x

4. Please work each part. (a) Discuss the existence or
non-existence of limx→0 2 sin 1 x − x 2 cos 1 x using the limit
theorems. (b) Let I be an open interval with a ∈ I and suppose that
f is a function defined on I\{a}. Suppose that limx→a (f(x) + D(x))
exists, where D(x) = χQ(x) is the Dirichlet function. Show that
limx→a f(x) does not exist.

(a) Rewrite the expression as an algebraic expression in x
tan(sin-1(x))
(b) Find sin(2x), cos(2x) and tan (2x) from the given
information
csc(x)=4, tan(x)<0

3. Use the definition of a limit (Definition 3.1.1) to show the
following: (a) limx→2 (x 2 + 2x − 5) = 3 (b) limx→1 (x 3 + 2x + 1)
= 4 (c) limx→0 (x 3 sin(e x 2 )) = 0

Find sin(x/2), cos(x/2), and tan(x/2) from the given
information.
Sin(x) = 24/25, 0° < x < 90°

use the intermediate value theorum to show that the following
functiom has a root.
f(x)= tan(x)+x-1
f(x)= tan(x)+x-4
f(x)= sec(x)+x-6

Prove the identity
1) sin(u+v)/cos(u)cos(v)=tan(u)+tan(v)
2) sin(u+v)+sin(u-v)=2sin(u)cos(v)
3) (sin(theta)+cos(theta))^2=1+sin(2theta)

find dy/dx. yo do not need to simplify.
1. 4cos(x)sin(y)+tan(x/y)=1+x+y
2. x/y=cosx
Please show work.

1. Use the given conditions to find the exact value of the
expression.
sin(α) = -5/3, tan(α) > 0, sin(α - 5π/3)
2. Use the given conditions to find the exact value of the
expression.
cos α = 24/25, sin α < 0, cos(α + π/6)
3. Use the given conditions to find the exact value of the
expression.
cot x = √3, cos x < 0, tan(x + π/6)
4. If α and β are acute angles such that...

A) Prove the trigonometric identity
(tan x + 2)^2 = sec^2 x + 4 tan x + 3
B) Use a sum-to-product identities to show that
cos(x + y) cos x cos y = 1 − tan x tan y.
C) Write the product as a sum
Sin12xSin4x

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