We want to find the maximum and minimum values of f(x, y) = 10x2 + 11y on the disk D: x2 + y2 < 1.

Now focus on the boundary of D, and solve for y2. Restricting f(x, y) to this boundary, we can express f(x, y) as a function of a single variable x. What is this function and its closed interval domain?

If you're just focusing on the boundary, it's the circle . Parameterize it by taking and , with . Then reduces to a univariate function :

Then you can find any extrema on the boundary by checking the critical points of .

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13