Question

Limx→a+​tan(bx)⋅limx→a+​tan(ax4)

lim⁡x→atan⁡(bx)⋅lim⁡x→asin⁡(x−a)x2−a2limx→a​tan(bx)⋅limx→a​x2−a2sin(x−a)​
A. tan⁡(ba)/tan⁡(a)​
B. tan(b)/tan(ba)​
C. tan(a)/tan(ab)​
D. tan(ab)/tan(ba)​

Answer 1

To evaluate the given limit expression, you need to apply the limit properties and simplify the expression step by step.

Step-by-step explanation:

To evaluate the limit of the given expression, we can apply the limit properties.

1. Start with the first limit: limx→a+ tan(bx).
2. Apply the second limit: limx→a+ tan(ax4).
3. Next, apply the third limit: limx→a tan(bx) · limx→a sin(x-a).
4. Finally, apply the fourth limit: limx→a tan(bx) · limx→a (x2-a2)/(sin(x-a)).

Once you have evaluated these limits, you can use the limit properties to simplify the expression and find the final result.