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Mathematics Solutions

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Mathematics
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Provide solution to the following questions:
1. Evaluate the following:
Solution
xsin3xdx
f=x g’=sin3x
f’=1 g=sin3x dx
Thus sin3x dx =|y=3x, dy=3, dx=1/3dy|
1/3cos ydy= 1/3cosy=1/3cos3x
xsin3xdx =-1/3xcos3x-1/3cos3x dx
-1/3xcos3x-1/3*1/3∫cosydy
=-1/3xcos3x+1/9sin3x+C
2. If , then for what value of α is A an identity matrix?
3. The line y = mx + 1 is a tangent to the curve y
2
= 4x .Find the value of m.
Given that the curve y=mx+1 and curve y
2
=4x, we solve this simultaneously;
Y=mx+1
Y
2
=4x

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Provide solution to the following questions: 1. Evaluate the following: Solution ∫xsin3xdx f=x g’=sin3x f’=1 g=∫sin3x dx Thus ∫sin3x dx =|y=3x, dy=3, dx=1/3dy| 1/3∫cos ydy= 1/3cosy=1/3cos3x ∫xsin3xdx =-1/3xcos3x-1/3∫cos3x dx -1/3xcos3x-1/3*1/3∫cosydy =-1/3xcos3x+1/9sin3x+C , then for what value of α is A an identity matrix? 2. If 3. The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m. Given that the curve y=mx+1 and curve y2=4x, we solve this simultaneously; Y=mx+1 Y2=4x Thus, (mx+1)2=4x We note that the tangent touches the curve, Therefore, the ...
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