How to solve these two question?

1.

The total differential approximation works in three-dimensional space, too. For example, consider the paraboloid 2 2 z=F93, =xly ( y) 22 32 at the point [1, 3, 5/4]. The total differential approximation to z = F(a;, y) near [1,3] is given by the formula F(m,y) a 5/4 + '3(1,3)(m 1) + %(1,3>(y 3). In fact, this gives the equation of the tangent plane to the surface at the point [1, 3, 5/4]. Now - = - a,= -- So we have the linear approximation to F(a:, y) near [1,3] : F(a:, y) z (1/2)*x+(2/3)*y-5/4 a . . Use this formula to approximate (to 3 decimal places) F(1.1,3.1) m - . Compute directly from the denition (to 3 decimal places) the value F(1.1,3.1) = -. In the previous questions, it was possible to calculate the value of the function exactly. But it is also possible to make mathematical deductions without knowing the function (which might be impossible or expensive to obtain), and instead only knowing the partial derivatives. Assume that the approval rating of 3 Prime Minister is given by the function A(d, e), where d is defence spending (in billions) and e is education spending (in billions). The output of the approval rating A(d, e) itself is a percentage between 0 and 100. It is desirable to predict how changes to defence and education spending impact upon the PM's approval. With current spending at do and co , the rate that approval (in percentage) changes with respect to defence spending (in billions) is measured by Newspoll to be the partial derivative ammeo) = 8.3 , so an increase in defence spending of 1 8d billion dollars will translate to an increase in approval of 8.3%. Similarly the rate that approval changes with respect to education spending is measured to be the partial derivative %(d0,e0) = 5.4. Hence by the total differential approximation, for [d, e] in the neighbourhood of [(10, e0] A(d, e) e A(d0, e0) + %(d0, e0)(d d0) + gfwo, e0)(e so). The current approval rating is A(d0, 80) = 55. If defence spending is decreased by 0.4 billion and education spending increased by 0.3 billion, then the approval rating approximately changes to %. Note: do not round your answer, approval rating is too important to be rounded