Question

Find the following limit. Is the function continuous at the point being approached?

ModifyingBelow lim With x right arrow pi divided by 4limx→π/4StartRoot cosecant squared x plus 2 tangent x EndRootcsc2^(x)+2tanx

Choose the correct answer below and fill in the answer box within your choice.

(Simplify your answer.)

A.

ModifyingBelow lim With x right arrow pi divided by 4limx→π/4StartRoot cosecant squared x plus 2 tangent x EndRootcsc^2(x)+2tanx=nothing,

and the function is not continuous at

xequals=StartFraction pi Over 4 EndFractionπ4.

B.

ModifyingBelow lim With x right arrow pi divided by 4limx→π/4StartRoot cosecant squared x plus 2 tangent x EndRootcsc^2 (x)+2tanx=nothing,

and the function is continuous at

xequals=StartFraction pi Over 4 EndFractionπ/4.

C.The limit does not exist, so the function is not continuous at

xequals=StartFraction pi Over 4 EndFractionπ/4.

Answer #1

Find an equation for the line tangent to the curve at the point
defined by the given value of t. Also, find the value of
StartFraction d squared y Over dx squared EndFractiond2ydx2
at this point.
x=secant^2 t−1
,
y=cos t;
t=negative StartFraction pi Over 3 EndFraction−π/3
Write the equation of the tangent line.
y=?xplus+?
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StartFraction d squared y Over dx squared EndFractiond2ydx2
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