







y=lnx+(1+ln2)/2 and y=x^2 
20190128 

From Mike: Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.
The course is about logarithm and root functions... how should I solve this problem? Answered by Penny Nom. 





Two curves 
20180923 

From Megan: How do i find the interception points of xy=2 and y=x+3? Many thanks! Answered by Penny Nom. 





The area of a region bounded by two curves 
20090107 

From Rogerson: Find the area, S, enclosed by the given curve(s) and the given line.
y = x^2  x  1, y = x+2 Answered by Harley Weston. 





The area enclosed by a curve and the xaxis 
20090104 

From Rogerson: Find the area, S, enclosed by the curve y = x^2 + 6x  5 and the xaxis in the interval 0≤x≤4. Answered by Harley Weston. 





The area bounded by 3 curves 
20080413 

From Sabahat: Hi, I have enclosed a diagram.
The diagram shows the curve y=(2x5)4. The point P has coordinates (4,81) and the tangent to the curve at P meets the xaxis at Q.
Find the area of the region (shaded in the diagram) enclosed between the curve, PQ and the xaxis . (Please note that the equation y is read as y=2x 5 whole raise to power 4.) Answered by Stephen La Rocque. 





Parameters 
20060915 

From Chase: What is the meaning of the word "parameters" when used in reference to Algebra. Answered by Penny Nom. 





An epicycloid 
20060410 

From Sharon: What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Answered by Stephen La Rocque and Penny Nom. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





Asymptotes 
20011109 

From Frank:
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom. 





Area between curves 
20010613 

From Phil:
question 1 find the area bound by the curves y = x^{2} + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x^{2} + y^{2} = 9 about the xaxis Answered by Harley Weston. 





The area between two curves 
20010508 

From Esther: Find the area of the region enclosed by the graphs of y = x^{3}6x and y = 2x between their points of intersection. Answered by Harley Weston. 





Length of a line 
19991010 

From Dagmara Sarudi: My question has to do with the length of a diagonal. This problem came up when I thought about the shortest distance between two points, for example walking from one point to another in my neighborhood. I can choose a zig zag route and assuming the blocks I walk are exactly the same length, it shouldn't matter what route I took, the distance I travel should still be the same when I reached my goal. If, on the other hand I could travel in a diagonal line, the distance would be shorter. But what if, in my zig zag motion, the sections get so small the route approaches a diagonal. Shouldn't it be that each separate section added together equals the value of the two original sides? Or would it suddenly equal the value of the diagonal (which, of course was shorter than the two sides added together)? What gives? Answered by Chris Fisher and Harley Weston.






Slopes of curved lines 
19990609 

From Stephen Ehrler: When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Answered by Harley Weston. 

