To find the limit of the function as y approaches -π/2, we first need to understand the behavior of the functions sec(y) and tan(y) near -π/2.

1. Rewrite the secant function: sec(y) = 1/cos(y)
2. Rewrite the tangent function: tan(y) = sin(y)/cos(y)

As y approaches -π/2, cos(y) approaches 0 from the right side, and sin(y) approaches -1.

3. Substitute these values into the expressions for sec(y) and tan(y):

sec(y) = 1/cos(y) = 1/0, which is undefined.
tan(y) = sin(y)/cos(y) = -1/0, which is also undefined.

Therefore, the limit of the function [sec y + tan y] as y approaches -π/2 does not exist.

Question

To find the limit of the function as y approaches -π/2, we first need to understand the behavior of the functions sec(y) and tan(y) near -π/2.

1. Rewrite the secant function: sec(y) = 1/cos(y)
2. Rewrite the tangent function: tan(y) = sin(y)/cos(y)

As y approaches -π/2, cos(y) approaches 0 from the right side, and sin(y) approaches -1.

3. Substitute these values into the expressions for sec(y) and tan(y):

sec(y) = 1/cos(y) = 1/0, which is undefined.
tan(y) = sin(y)/cos(y) = -1/0, which is also undefined.

Therefore, the limit of the function [sec y + tan y] as y approaches -π/2 does not exist.

Knowee AI · Accepted Answer

To find the limit of the function as y approaches -π/2, we first need to understand the behavior of the functions sec(y) and tan(y) near -π/2.

1. Rewrite the secant function: sec(y) = 1/cos(y)
2. Rewrite the tangent function: tan(y) = sin(y)/cos(y)

As y approaches -π/2, cos(y) approaches 0 from the right side, and sin(y) approaches -1.

3. Substitute these values into the expressions for sec(y) and tan(y):

sec(y) = 1/cos(y) = 1/0, which is undefined.
tan(y) = sin(y)/cos(y) = -1/0, which is also undefined.

Therefore, the limit of the function [sec y + tan y] as y approaches -π/2 does not exist.

Determine lim y→− π 2 [sec y + tan y]