Evaluate
Let ( I = \int (7x - 2)\sqrt{3x + 2} , dx ). Use substitution: ( u = 3x + 2 \implies du = 3 dx \implies dx ___ _____ ______ ________ ___ ____ ______ ______ ______ ________ __________.
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Solve the following differential equation
given Y(0) = 4
5. If Z = f(x,y) = xy
Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is, x+y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.
Evaluate
Consider the following two matrices
A =
B =
(i) Find the rank of 'A' and 'B'
(ii) Show that (AB)⁻¹ = B⁻¹ A⁻¹
(iii) Show that (A⁻¹)⁻¹ = A
(iv) Show that (B⁻¹)⁻¹ = B
An individual consumer consumes two commodities X₁ & X₂. The utility function is
The price of commodity one is P₁ = Rs.3.00, the price of commodity two is P₂ = Rs.4.00, the individual's income per period is Rs.108. Determine the utility maximizing level of X₁ & X₂ and derive the demand curves for the two commodities.
Let Z = f(x,y) = 3x³-5y²- 225x + 70y + 23.
(i) Find the stationary points of z.
(ii) Determine if at these points the function is at a relative maximum, relative minimum, infixion point, or saddle point.
Decomposable matrix
Explain the concept of maximum value function.