Use properties of limits to find the indicated limit. It may be necessary to rewrite the expression before limit properties can be applied.

limx→1
x^2+3x−4x^2−1

The required value is -1.

Step-by-step explanation:

Since we have given that

Since , it is necessary to rewrite the expression before limit properties as there is like terms exists.

So, it becomes,

Hence, the required value is -1.

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is