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- What is the long term behavior of your hand drawn solution; that is, what is lim t-> infinity M(t) equal to?1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞ 6e−6x
- Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the definition: m=lim->a f(x)-f(a)/x-a 2)using the equation: m=lim->0 f(a+h)-f(a)/hSuppose g(x)<h(x)forx∈(0,1)∪(1,2) both limx→1g(x)andlimx→1h(x) exist. Must limx→1g(x)<limx→1h(x)? true or falseIf f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ? Is f(x) continuous at 3?
- Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞ 7x2 + 10x − 1/2x2 − 2x ______________If a rectangle has its base on the x-axis and two vertices on the curve y=e^-x^2, show that the rectangle has the largest possible area when the two vertices are at the points of inflection of the curve.Use the definition of the derivative to evaluate lim In(2+h) - In(2)/h h approaches 0
- Compute the lim(x,y)->(0,0) (4x2y)/(x2+y2)1/2We consider the rational function f(x) = p(x)/ q(x) = 2x ^2 + cx − 4c / x^2 − x − 2 . Here c is an unknown constant. If the limit L = limx→2 f(x) is a finite number, then what is c?The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a real solution