1) Limit theta approaching zero
sin squared theta/ tan theta
2) Lim x appraoches zero
x + sin x/x
x + sin x/x = x/x + sinx/x
0 + 1 =1
My answer : 1 Is this correct
Yes, your answer is correct.
To find the limit as x approaches zero for the expression x + sin(x)/x, you correctly simplified the expression to obtain x/x + sin(x)/x. Since x/x equals 1 for any nonzero value of x, the expression simplifies further to 1 + sin(x)/x.
Now, as x approaches zero, sin(x)/x is a well-known limit and evaluates to 1. Therefore, the expression becomes 1 + 1 = 2.
However, it seems there was an error in your work when you wrote 0 + 1 = 1. The correct evaluation is 1 + 1 = 2.