Please help to solve the following questions

Thank you very much

Some question I don't why I mixed up the positive and negative signs.

If you see a limit tending to -infty, use a substitution of y=-x for the very first step to make things easier.

46 should be manageable now.

48 is in a form of "sqrt + sqrt" (well, x is just sqrt(x^2), kind of. Beware of signs). You should know what to do.

For 50, hopefully when you see sine, you are immediately inspired, at some point, to use "limit as A tends to 0 sinA/A = 1". Now where to apply it is not yet apparent (but still you need to know this technique for diff. by first principles).

Here's a well-known enough limit that isn't taught, but I just use it anyway (

"limit as A tends to 0 of (1-cosA)/A = 0"

As to why this is true, multiply and divide (1+cosA) and see what happens.

Solution to 50 in a bit.

EDIT: Solution to 50 - https://www.docdroid.net/afWv6mC/limits-2-pdf

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Thank you very much for your kind assistance.

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