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Find the angle between the pairs of lines with direction ratios proportional to 2, 2, 1 and 4, 1, 8 .
Concept: undefined >> undefined
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Concept: undefined >> undefined
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Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Concept: undefined >> undefined
Find the angle between the pairs of lines with direction ratios proportional to 1, 2, −2 and −2, 2, 1 .
Concept: undefined >> undefined
Show that f(x) = cos2 x is a decreasing function on (0, π/2) ?
Concept: undefined >> undefined
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Concept: undefined >> undefined
Find the angle between the pairs of lines with direction ratios proportional to a, b, c and b − c, c − a, a − b.
Concept: undefined >> undefined
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Concept: undefined >> undefined
Find the angle between two lines, one of which has direction ratios 2, 2, 1 while the other one is obtained by joining the points (3, 1, 4) and (7, 2, 12).
Concept: undefined >> undefined
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Concept: undefined >> undefined
Show that f(x) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?
Concept: undefined >> undefined
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Concept: undefined >> undefined
Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?
Concept: undefined >> undefined
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Concept: undefined >> undefined
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Concept: undefined >> undefined
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Concept: undefined >> undefined
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Concept: undefined >> undefined
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Concept: undefined >> undefined
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Concept: undefined >> undefined
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Concept: undefined >> undefined
