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Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?
Concept: undefined >> undefined
Find the angle between the following pair of line:
\[\frac{x - 5}{1} = \frac{2y + 6}{- 2} = \frac{z - 3}{1} \text{ and } \frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 6}{5}\]
Concept: undefined >> undefined
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Find the angle between the following pair of line:
\[\frac{- x + 2}{- 2} = \frac{y - 1}{7} = \frac{z + 3}{- 3} \text{ and } \frac{x + 2}{- 1} = \frac{2y - 8}{4} = \frac{z - 5}{4}\]
Concept: undefined >> undefined
Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ?
Concept: undefined >> undefined
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Concept: undefined >> undefined
Show that f(x) = e2x is increasing on R.
Concept: undefined >> undefined
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Concept: undefined >> undefined
Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?
Concept: undefined >> undefined
Find the angle between the pairs of lines with direction ratios proportional to 5, −12, 13 and −3, 4, 5
Concept: undefined >> undefined
Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?
Concept: undefined >> undefined
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Concept: undefined >> undefined
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
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
