Sir, In the first example, for DCT, if theta=5pi/6, then the inequality for the last two wouldn't hold.
@DrMathaholic3 жыл бұрын
Yes, you are correct dude.. i was bit casual 😔 its only correct till 0 to π/2 and from π/2 to π inequality reverses... So the best way is substitute π-theta= x.
@nighatlone773 жыл бұрын
The set [a, b] belogs to [c, d] is A) closed set B) open set. (C) nether closed nor an open set (D) neither an interval nor an open set
@DrMathaholic3 жыл бұрын
Closed set
@nighatlone773 жыл бұрын
@@DrMathaholic thank u sir....
@helloworld-hv9oy3 жыл бұрын
Sir for the last questions is that test required ,beacuse we can directly evaluate that integral ? One more doubt ,it seems that for the limit test the convergence and divergence of f(x) depends upon the function g(x) we choose ...so can it be possible that there are two such functions and different answers come ?
@DrMathaholic3 жыл бұрын
If you can evaluate directly then no problem at all. One can choose different different g(x) no problem in that, but the good thing is nature of f(x), whether it convergent or divergent, does not changes.
@helloworld-hv9oy3 жыл бұрын
@@DrMathaholic okay sir thank you !
@legendgaming80202 жыл бұрын
Sir how we solve this sum>>>>. 1/(1+x)x^1/2 converge or devearge i
@legendgaming80202 жыл бұрын
Limit x =0 to infinity
@DrMathaholic2 жыл бұрын
rewriting as: root(x)/(x(x+1)) = root(x)(1/x - 1/(x+1)) = root(x)/x - root(x)/(x+1) . for first term, split the integration 0 to 1 and 1 to infinity. for 1 to infinity 1/root(x) diverges. so i think answer is divergent.
@SumitGaming-2 жыл бұрын
Sir in 3rd part 9:29 ,it converges
@DrMathaholic2 жыл бұрын
How? 🤔🤔🤔 1/x^3 is diverging right?
@SumitGaming-2 жыл бұрын
@@DrMathaholic sorry .you are right
@DrMathaholic2 жыл бұрын
@@SumitGaming- 🙌🙌🙂
@krishnadehrawala4422 жыл бұрын
Sir we can apply any test from limit and direct ?
@DrMathaholic2 жыл бұрын
Yes , just check the conditions..if the functions satisfies the conditions in that theorem then you can apply the respective test. If one test fails then try for second one..