204 results authored by Bill Foster - search across all users.
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Question in Bill's workspace
When are vectors \boldsymbol{A,\;B} perpendicular?
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Question in Bill's workspace
Given vectors \boldsymbol{A} and \boldsymbol{B}, find their inner product.
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Question in Bill's workspace
Given vectors \boldsymbol{A,\;B}, find \boldsymbol{A\times B}
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Question in Bill's workspace
Determine if various combinations of vectors are defined or not.
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Question in Bill's workspace
Given vectors \boldsymbol{A,\;B}, find the angle between them.
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Question in Bill's workspace
Differentiate (a+bx) ^ {m} \sin(nx)
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Question in Bill's workspace
Differentiate x^m\cos(ax+b)
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Question in Bill's workspace
Differentiate \sin(ax+b) e ^ {nx}.
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Question in Bill's workspace
Differentiate (ax+b)^m(cx+d)^n using the product rule. The answer will be of the form (ax+b)^{m-1}(cx+d)^{n-1}g(x) for a polynomial g(x). Find g(x).
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Question in Bill's workspace
Differentiate x ^ m(ax+b)^n using the product rule. The answer will be of the form x^{m-1}(ax+b)^{n-1}g(x) for a polynomial g(x). Find g(x).
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Question in Bill's workspace
The derivative of \displaystyle \frac{ax+b}{cx^2+dx+f} is \displaystyle \frac{g(x)}{(cx^2+dx+f)^2}. Find g(x).
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Question in Bill's workspace
The derivative of \displaystyle \frac{ax+b}{\sqrt{cx+d}} is \displaystyle \frac{g(x)}{2(cx+d)^{3/2}}. Find g(x).
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Question in Bill's workspace
Differentiate the function f(x)=(a + b x)^m e ^ {n x} using the product rule. Find g(x) such that f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x).
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Question in Bill's workspace
Differentiate the function (a + b x)^m e ^ {n x} using the product rule.
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Question in Bill's workspace
Differentiate x ^m \sqrt{a x+b}.
The answer is in the form \displaystyle \frac{x^{m-1}g(x)}{2\sqrt{ax+b}}
for a polynomial g(x). Find g(x). -
Question in Bill's workspace
Differentiate f(x) = x^m(a x+b)^n.
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Question in Bill's workspace
Rotate the graph of y=a\ln(bx) by 2\pi radians about the y-axis between y=c and y=d. Find the volume of revolution.
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Question in Bill's workspace
Rotate y=a(\cos(x)+b) by 2\pi radians about the x-axis between x=c\pi and x=(c+2)\pi. Find the volume of revolution.
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Question in Bill's workspace
Evaluate \int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx, \int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx, \int_0^{r}x ^ {2}e^{t x}\;dx
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Question in Bill's workspace
Evaluate \int_0^{\,m}e^{ax}\;dx, \int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx.
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Question in Bill's workspace
Spearman rank correlation calculated. 10 paired observations.
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Question in Bill's workspace
Spearman rank correlation calculated. 8 paired observations.
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Question in Bill's workspace
Calculate the Pearson correlation coefficient on paired data and comment on the significance.
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Question in Bill's workspace
Calculate the Pearson correlation coefficient on paired data and comment on the significance.
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Question in Bill's workspace
Elementary examples of multiplication and powers of complex numbers. Four parts.
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Question in Bill's workspace
Inverse and division of complex numbers. Four parts.
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Question in Bill's workspace
Multiplication of complex numbers. Four parts.
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Question in Bill's workspace
Find p and q such that ax^2+bx+c = a(x+p)^2+q.
Hence, or otherwise, find roots of ax^2+bx+c=0.
Includes a video which shows how to solve a quadratic by completing the square.
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Question in Bill's workspace
Express \displaystyle a \pm \frac{c}{x + d} as an algebraic single fraction.
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Question in Bill's workspace
Express \displaystyle b+ \frac{dx+p}{x + q} as an algebraic single fraction.