1 Crore+ students have signed up on EduRev. Have you? 
Differentiating both sides w.r.t. x,
Let f(x) = x – [x], for every real number x, where [x] is the integral part of x. Then
[∵ x is an odd function]
Thus, putting value in equation (1) we get
For which of the following values of m, is the area of the region bounded by the curve y = x – x^{2} and the line y = mx equals 9/2?
The two curves meet at
or (1  m)^{3} = 27 ,
∴ m = 2
But if m >1 then 1– m is – ive, then
Let f (x) be a nonconstant twice differentiable function definied on ( ∞,∞) such th at f (x) = f (1 – x) and
∴f (x) is a non constant twice differentiable function such that f (x) = f (1– x) ⇒ f '(x) = – f ' (1 – x) ...(1)
but given that
Hence, f '(x) satisfies all conditions of Rolle's theorem for So there exists at least one point and at least one point
Such that
f "(C_{1}) = 0 and f "(C_{2}) = 0
Area of the region bounded by the curve y = ex and lines x = 0 and y = e is
The area bounded by the curve y = e^{x} and lines x = 0 and y = e is as shown in the graph.
Also required area
Adding equations (1) and (2), we get
[as integrand is an even function]
The value(s) of
Let f be a realvalued function defined on the interval (0, ∞) by Then which of the following statement(s) is (are) true?
We have
and f '(x) has finite continuous
Which does not exist at the points where
∴ f '(x) is not differentiable.
∴ (a) is false but (b) is true
Let S be the area of the region enclosed by , y = 0, x = 0 and x = 1; then
First of all let us draw a rough sketch of y = e–x.
At x = 0, y = 1 and at x = 1, y = 1/e
∴ is decreasing on (0, 1)
Hence its graph is as shown in figure given below
Now, S = area exclosed by curve = ABRO
and area of rectangle ORBM = 1/e
Now S < area of rectangle APSO + area of rectangle CSRN
The option(s) with the values of a and L that satisfy the following equation is(are)
where ‘a’ can take any even
value.
Let f(x) = 7tan^{8}x + 7tan^{6}x – 3tan^{4}x – 3tan^{2}x for all Then the correct expression(s) is(are)
f(x) = 7 tan^{8}x + 7tan^{6}x – 3tan^{4}x – 3tan^{2}x
= (7tan^{4}x – 3) (tan^{4}x + tan^{2}x)
= (7tan^{6}x – 3tan^{2}x) sec^{2}x
= 1/12
then the possible values of m and M are
∴ Only (d) is the correct option.
all x > 0. Then
∴ f is an incr easing function.
Hence (b) and (c) are the correct options.
132 docs70 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
132 docs70 tests





