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Pages:
1 page/≈550 words
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Level:
APA
Subject:
Mathematics & Economics
Type:
Essay
Language:
English (U.S.)
Document:
MS Word
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Topic:
Mathematics calculus, algebra and ode. Mathematics & Economics Essay (Essay Sample)
Instructions:
Mathematics task
source..Content:
Solutions
1. Evaluate the following
xsin3xdx
Soln
Integration by parts;
udv=uv-vdu
Liate-order of integration
Let u=x and dv=sin3xdx;du=dx;v=sin3xdx=-13cos3x
udv=uv-vdu
xsin3xdx=-13xcos3x--13cos3xdx
=-13xcos3x+13cos3xdx
=-13xcos3x+13∙13sin3x+c
=-13xcos3x+19sin3+c
2. If A=cosα-sinαsinα-cosα, then for what value of α is A an identity matrix?
Identity matrix is given by 1001 , then determinant1001=1
Therefore if the matrix A is an identity matrix then its determinant is also 1
Determinant A=cosα-sinαsinα-cosα=-cos2α-sin2α
-cos2α-sin2α=1;
cosα-sinαsinα-cosα=1001;cosα=1,Thereforeα=0
3. The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m.
mx+12=4x ⇒m2x2+1+2mx-4x
=m2x2+2m-4x+1=0
=2m-42-4m2×1=0
=4m2+16-16m-4m2=0
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