Question

For what values of a and b is the following equation true? lim x→0 (sin(2x)/x^3 + a + b/x^2)=0

Answer #1

1. if lim
x->infinity+ (5+2X)/(9-6X)=??
2. what is the value for the same equation if lim x approaches
to negative infinity???
3. if lim x approaches to positive infinity then evaluate the
equation (4X+7)/(5X^2-3X+10)
4. What would be the value of the above mentioned equation is
lim x approaches to negative infinity

x’+2x=sin(t), x(0)=1
solve the first order differential equation.

Show that the equation f(x) = sin(x) - 2x = 0 has exactly one
solution on the interval [-2,2]

Suppose that S(x)=∫x0
sin(t5)dt
1. Compute S(0)
2. Compute the derivative S ′(x)
3. Evaluate lim x→0 (S(x)/
x6)

Lim x-0 (1+sin5x)^1/2x
le hopitals

(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

Consider the curve given by the equation
sin(?−?)=2?+?sin(x−y)=2x+y. The equation defines ?y as a function
?(?)y(x) near (0,0)(0,0).
(a) Find the equation of the tangent line to this curve at the
point (0,0)(0,0).
(b) Find ?″(0)y″(0).

lim x→0 ((1+sin)^cotx-e)/tanx
How can I solve it?
lim x→0 ((1+sinx)^cotx-e)/tanx
I missed x

a.) Find the following limit.
lim x→−∞ x^3 - sqrt(4x^6-3x)/7x^3+x
b.) Sketch the graph of a function f(x) that has all of the
following features:
f ' (x) > 0 on the intervals (−∞, −4) ∪ (3,∞).
f ' (x) < 0 on the intervals (−4, −1) ∪ (−1, 3).
f '' (x) > 0 on the intervals (−∞, −4) ∪ (−4, −2) ∪ (−1,
4).
f '' (x) < 0 on the intervals (−2, −1) ∪ (4,∞).
x-intercepts when...

1. Evaluate the limit using L'Hospital's rule if necessary
lim x→∞ (1+ 12 / x)^x/1
2. In which limits below can we use L'Hospital's Rule?
lim x→π/5 sin(5x) /5x−π
lim x→−∞ e^−x / x
lim x→0 2x/ cotx
lim x→0 sin(3x) / 3x
I Need help with both questions please! thank you so much.

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