1.) limx-->0; (x + sinx) / (x + cosx)
2.) limx-->infinite; (e^-x)cosx
3. limx-->0; (xcscx + 1) / (xcscx)
thanks
1.) limx-->0; (x + sinx) / (x + cosx)
dividing the top and bottom by x
=limx-->0; [1 + (sinx)/x] / [1 + (cosx)/x]
limx-->0 (sinx)/x=1 ;limx-->0 (cosx)/x=0
then continue... u should get 2
2.) limx-->infinite; (e^-x)cosx
=limx-->infinite; (cosx)/e^x
i think it is zero since limx-->infinite; e^x=infinite, but might also be undefined if x=n pi/2
3.) limx-->0; (xcscx + 1) / (xcscx)
divide top and bottom by xcsc+1
=limx-->0; [1+ (sinx)/x] / [(xcscx)/(xcscx)]
=limx-->0; [1+ (sinx)/x]
limx-->0 (sinx)/x=1; u should get 2