GroupHomework #5

Let NiMvLUkiZkc2IjYjSSJ4R0YmLUkkY29zR0YmRic=.a) Find values of the constants a and b so that the lionear function NiMvLUkiTEc2IjYjSSJ4R0YmLCZJImFHRiYiIiIqJkkiYkdGJkYrRihGK0Yr has the properties L(0)=f(0) and L'(0)=f'(0).b) Find the value of the constant c for which the quadratric function NiMvLUkiUUc2IjYjSSJ4R0YmLCYtSSJMR0YmRiciIiIqJkkiY0dGJkYsKiRGKCIiI0YsRiw= has the properties Q(0)=f(0), Q'(0)=f'(0) and Q''(0)=f''(0).c) Find the value of the constant d for which the cubic function NiMvLUkiQ0c2IjYjSSJ4R0YmLCYtSSJRR0YmRiciIiIqJkkiZEdGJkYsKiRGKCIiJEYsRiw= has the properties C(0)=f(0), C'(0)=f'(0), C''(0)=f''(0), and C'''(0)=f'''(0).d) Plot f, L, Q, and C on the same axes over the interval [-4,4].e) Find an interval over which NiMyLUkkYWJzR0kqcHJvdGVjdGVkR0YmNiMsJi1JImZHNiI2I0kieEdGKyIiIi1JIkxHRitGLCEiIi1JJkZsb2F0R0YmNiRGLkYx.f) Find an interval over which NiMyLUkkYWJzR0kqcHJvdGVjdGVkR0YmNiMsJi1JImZHNiI2I0kieEdGKyIiIi1JIlFHRitGLCEiIi1JJkZsb2F0R0YmNiRGLkYx.g) Find an interval over which NiMyLUkkYWJzR0kqcHJvdGVjdGVkR0YmNiMsJi1JImZHNiI2I0kieEdGKyIiIi1JIkNHRitGLCEiIi1JJkZsb2F0R0YmNiRGLkYx.

Find the equation of the line that is tangent to NiMvJSJ5RyomLCYqJCklInhHIiIlIiIiRitGK0YrRitGKSEiIg== at more than one point.

a) Verify that NiMvSSJ5RzYiLCYqKEkiQUdGJSIiIi1JJGV4cEdGJTYjLCQqJiIiJEYpSSJ0R0YlRikhIiJGKS1JJHNpbkdGJTYjKiYiIiNGKUYwRilGKUYpKihJIkJHRiVGKUYqRiktSSRjb3NHRiVGNEYpRik= solves the differential equation y'' + 6 y' + 13 y = 0.b) Find the solution to the initial value problem y'' + 6 y' + 13 y = 0 and y(0)=7 and y'(0)=10.

(a) Use the formula for the area of a circle of radus NiMlInJH, NiMvJSJBRyomJSNQaUciIiIqJCUickciIiNGJw==, to find NiMqJiUjZEFHIiIiJSNkckchIiI=.(b) The result from part (a) should look familiar. What does NiMqJiUjZEFHIiIiJSNkckchIiI= represent geometrically? Draw a picture on your printout.(c) Use the difference quotient to explain the observation you made in part (b)(d) Does the same rule work for a square? Why do you think this is so?