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Explain whether each statement is true or false. Please give short explanation why and if false, please give an example.
a) The maximum of a function that is continuous on a closed interval can occur at two different values in the interval.
b) If a function is continious on a closed interval, then it must have a minimum on the interval.
c) If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x) + k where k is a constant.
d) If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x-k), where k is a constant.
f(z) is defined by the equations: f(z)=1 when y 0, and C is the arc from z=-1-i to z=1+i along the curve y = x^3. The answer is given as 2+3i.
Find the point on the graph of y= e^x at which the curvature is the greatest. Write the equation for the surface generated by revolving the curve x^2 - 2y^2 = 1 about the y-axis. Describe the surface
Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations graph) to determine if the system has no solution or an infinite number of solutions.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
Digit probability A young girl gave a young man her phone number during a hurried parting. The young man remembers the 7 digits of her phone number
Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.
Until recently, with the advent of cellular phones, modems, and pagers, the area codes in the United States and Canada followed a certain system
If a system of nonlinear equations contains one equation whose graph is a circle and another equation whose graph is a line, can the system have exactly one solution?
Find the natural domain of the given functions.
If Player A gets to throw 2 darts and Player B gets to throw 5 darts, how do you calculate the probability of Player A or Player B getting the highest total score?
Using the appropriate substitution method and the quotient rule find the integral of: Integral: 1+tanx/1-tanx dx
Let alpha = {x_1, x_2, ..., x_n} be an arbitrary orthonormal basis for V. Prove that T is orthogonal iff [T]_alphaalpha is an orthogonal matrix.
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