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# 1sol - Calculus I Assignment 1 Question 1 Step 1 We know...

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Calculus I Assignment # 1 Question 1 Step 1. We know volume V of a cube of side length x is V= x 3 . Step 2. Two applications of Pythagora's Theorem on appropriately chosen triangles will give us = d 2 + x 2 + x 2 x 2 2 . Thus, the length of the diagonal, d, in terms of the side length x simplifies to = d 2 3 x 2 or = d 3 x ( d is a physical quantity, hence non-negative). Step 3. We can isolate for x from above equation to get x in terms of d = x d 3 Step 4. Plugging the above into our original volume formula gives V in terms of d = V d 3 3 This is the function we define in maple: > V:=d->d^3/(3^(3/2)); := V d 1 9 d 3 3 To evaluate volume V at diagonal length d=1.2: > V(1.2); evalf(%); 0.1920000000 3 0.3325537551 the evalf command performed on % gives a decimal approximation of the previously entered command Question 2 We can define a bunch of functions, assigning different values to the parameter c > y1:=x->abs(x)/sqrt(1-x^2); := y1 x x 1 x 2 > y10:=x->abs(x)/sqrt(10-x^2); := y10 x x 10 x 2 > y100:=x->abs(x)/sqrt(100-x^2); := y100 x x 100 x 2 > plot([y1,y10,y100],-12..12,0..10,colour=[blue,red,green]);

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1sol - Calculus I Assignment 1 Question 1 Step 1 We know...

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