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Using simplex method, maximize Z(x, y)=7x+y subject to constraints 3x+4y ≤ 12, y-x≤2. x, y ≥0.

Using simplex method, maximize F= 18x+8y subject to x+2y≤25, 3x+2y≤28, x,y≥0.

A residential student of a school is putting the following questions to his roommates. Answerthese questions.a. What is the relation between continuityand differentiability of a function at a point...

Find from first principle, the derivative of ln(sin x/a).

At what angle does the curve y(1+x)=x cut the x-axis?

State Rolle's theorem. Verify that the function f(x)= x(x-3)^2 on [0,3] satisfies conditions of Rolle's theorem and find C prescribed in the theorem.

Find the derivative of (sinh(x/a) + cosh (x/a)) ^ nx.