निम्नलिखित श्रेणी के अभिसरण की जाँच कीजिए:
i)
ii)
हम दी गई श्रेणियों की अभिसरण (convergence) की जाँच करते हैं: ### (i) श्रेणी \[ S = \frac{3\times 4}{5^2}+\frac{5\times 6}{7^2}+\frac{7\times 8}{9^2}+\cdots \] #### परीक्षण 1. श्रेणी के सामान्य पद को देखेँ: \[ a_n = \frac{(2n+1)(2n+2)}{(2n+3)^2} \] 2. सीमा जाँच: \[ \lim_{n \to \infty} \frac{(2n+1)(2n+2)}{(2n+3)^2} \] सबसे उच्च घातांक के साथ सीमा निकालते हैं: \[ \lim_{n ______ ________ ___ ___ ________ ______ _________.
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Let (a) be a sequence defined as show that (an) converges
Examine the function f : R→R defined by
for continuity on R. If it is not continuous at any point of R, find the nature of discontinuity there. (x+1)x+0 9-59-1
Find lim
ज्ञात कीजिए।
Are the following statements true or false? Give reasons for tour answers.
a) -2 is a limit point of the interval 1-3,2].
b) The series is divergent.
The function, f(x)=sin² x is uniformly continuous in the interval [0, π).
d) Every continuous function is differentiable.
e) The function f defined on R by
is irrational Is integrable in the interval [2,3].
निम्नलिखित श्रेणी के अभिसरण की जाँच कीजिए:
i)
ii)
Check whether the function given by:
has local maxima and local minima.
For the function, defined over [1,5], verify:
where P is the partition which divides [1.5] into four equal intervals.