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`f(x) = (x+1) (x+2)^(1/3), x>=-2` .
Concept: undefined >> undefined
`f(x)=xsqrt(32-x^2), -5<=x<=5` .
Concept: undefined >> undefined
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f(x) = \[x^3 - 2a x^2 + a^2 x, a > 0, x \in R\] .
Concept: undefined >> undefined
A unit vector \[\vec{a}\] makes angles \[\frac{\pi}{4}\text{ and }\frac{\pi}{3}\] with \[\hat{i}\] and \[\hat{j}\] respectively and an acute angle θ with \[\hat{k}\] . Find the angle θ and components of \[\vec{a}\] .
Concept: undefined >> undefined
f(x) = \[x + \frac{a2}{x}, a > 0,\] , x ≠ 0 .
Concept: undefined >> undefined
f(x) = \[x\sqrt{2 - x^2} - \sqrt{2} \leq x \leq \sqrt{2}\] .
Concept: undefined >> undefined
If two vectors \[\vec{a} \text{ and } \vec{b}\] are such that \[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 1 \text{ and } \vec{a} \cdot \vec{b} = 1,\] then find the value of \[\left( 3 \vec{a} - 5 \vec{b} \right) \cdot \left( 2 \vec{a} + 7 \vec{b} \right) .\]
Concept: undefined >> undefined
f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .
Concept: undefined >> undefined
f(x) = (x \[-\] 1) (x \[-\] 2)2.
Concept: undefined >> undefined
If \[\vec{a}\] is a unit vector, then find \[\left| \vec{x} \right|\] in each of the following.
\[\left( \vec{x} - \vec{a} \right) \cdot \left( \vec{x} + \vec{a} \right) = 8\]
Concept: undefined >> undefined
`f(x)=xsqrt(1-x), x<=1` .
Concept: undefined >> undefined
If \[\vec{a}\] is a unit vector, then find \[\left| \vec{x} \right|\] in each of the following.
\[\left( \vec{x} - \vec{a} \right) \cdot \left( \vec{x} + \vec{a} \right) = 12\]
Concept: undefined >> undefined
f(x) = \[- (x - 1 )^3 (x + 1 )^2\] .
Concept: undefined >> undefined
Find \[\left| \vec{a} \right| \text{ and } \left| \vec{b} \right|\] if
\[\left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) = 12 \text{ and } \left| \vec{a} \right| = 2\left| \vec{b} \right|\]
Concept: undefined >> undefined
The function y = a log x+bx2 + x has extreme values at x=1 and x=2. Find a and b ?
Concept: undefined >> undefined
Show that \[\frac{\log x}{x}\] has a maximum value at x = e ?
Concept: undefined >> undefined
Find \[\left| \vec{a} \right| \text{ and } \left| \vec{b} \right|\] if
\[\left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) = 8 \text{ and } \left| \vec{a} \right| = 8\left| \vec{b} \right|\]
Concept: undefined >> undefined
Find \[\left| \vec{a} \right| and \left| \vec{b} \right|\] if
\[\left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) = 3\text{ and } \left| \vec{a} \right| = 2\left| \vec{b} \right|\]
Concept: undefined >> undefined
Find the maximum and minimum values of the function f(x) = \[\frac{4}{x + 2} + x .\]
Concept: undefined >> undefined
Find \[\left| \vec{a} - \vec{b} \right|\] if
\[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 5 \text{ and } \vec{a} \cdot \vec{b} = 8\]
Concept: undefined >> undefined
