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Answered a Question in Math
`a(t) = sin(t) + 3cos(t)`
`v(t) = cos(t) + 3sin(t) + a`
`Now, v(0) = 2`
`Thus, 2 = cos(0)+3sin(0)+a`
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Answered a Question in Math
`f'(x) = cos(x)  (1x^2)^(1/2)`
`f(x) = sin(x)  sin^1(x) + c`
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Answered a Question in Math
`f'(x) = 2e^x + sec(x)tan(x)`
`f(x) = 2e^x + sec(x)`
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Answered a Question in Math
`f''(x) = 1  6x + 48x^2`
`f'(x) = x  3x^2 + 16x^3 + a`
`Now, f'(0) = 2`
`i.e. 2 = a`
`Thus, f'(x) = x ...

Answered a Question in Math
`f''(x) = 2x^3 + 3x^2  4x + 5`
`or, f'(x) = {(1/2)x^4} + x^3  2x^2 + 5x + a`
`or, f(x) = {(1/10)*x^5} + (x^4/4) ...

Answered a Question in Math
`f''(x) = x^2`
`f'(x) = x^1 + a`
`f(x) = lnx + ax + b`
`Now, f(1) = f(2) = 0`
`thus, a + b = 0`
... 
Answered a Question in Math
L.H.S
`(tan^2(theta))/sec(theta) = tan^2(theta)*cos(theta) = tan(theta)*cos(theta)*{tan(theta)} =`
... 
Answered a Question in Math
Let the standard quality version downloaded be 'x'
Thus, total size of high quality version downloaded = 2.6*x
Thus,...

Answered a Question in Math
`g(t) = t^4 + t^3 + t^2 + 1`
`or, g'(t) = 4t^3 + 3t^2 + 2t`
`or, g'(t) = t(4t^2 + 3t + 2)`
` g'(t) = 0`
... 
Answered a Question in Math
Since this is a `(oo)/(oo)` form
Thus, applying L'Hospital's rule we get
`lim_(x>oo)(5x^2)/(x+3) =...
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