N+ Assignmen Abstract Algeb 7.3. Show that (a). f(z) = x - iy2 is differentiable only at y = -1/2 and f'(z) = 1,
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- Estimate f(5.03) for f as in the figure. y y=f(x) (10, 4) Tangent line (4, 2) (Give your answer to three decimal places.) f(5.03) =For the function f(x,y)= x^2 +2y^2 Use the first derivative test to determine if the function is concave or convex.Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to approximate f(1.02, -1.97) without a calculator.
- The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2.x + y = 3 is given by T(x, y) 2x2 + 2x + 5y. Find the lowest temperature on the curve using: Second Derivative TestQ4: (1 zero? s) In what directions is the derivative of f(x,y) = (x - y)/(x² + y²) at P(1, 1) equal to 05: (12 Marks) Find naram darEX: Find the F.T. of the triangular pulse: g(t) = AA (+) Sols Apply differentiation property of F-T g(t) = 2A S(t+1)_4A S(t) + 2A S(t-I) The F. I for the both sides gives. (jw)² G (w) = 2A (NE_2 +2²) (e j들 (JW)³&(W) = 4A (2 ² + 2² (e 2 G(W) = -4A whe - 8A w²t -₁) 8A ( cos 뜰 -1) = 82 (1-005) 2 sin wt 4 At sin wt 2 Wt 4 2 3/4 N 2A T ZA 0 0 8(1)-A(+) =9c How did he get the value inside the circle Hes -9C2A ہم تم at ot