1.

Evaluate the limit of (x + sin 2x)/(x - sin 2x) as x approaches 0a. None of these b. 48 C. 16 d. 32 e. 68Given the Fourier series in Cosine form, f(t) = 5 cos 40nt + cos 60nt. What is the frequency of the fundamental?a. None of these b. 10 C. 40 d. 20 e. 30Determine the area of the region bounded by the parabola y = 9 - x^2 and the line x + y = 7.\fOne of the equal interior angles of an isosceles triangle is 58.250. If the area of the triangle is 68 sq.m, find the length of the shortest sidea. None of these b. 13 C. 11 d. 12 e. 10If Newton-Raphson method is used to solve the equation f(x) = x - 5x + 6x -8 =0. Taking the initial guess as x = 5, the solution obtained at the end of the first iteration is\fIt is an equation in the form a(d y/dx?) +b(dy/dx) + cy = 0, where a, b, and c are constants. Select one: O a. exact differential equation with constant coefficients O b. linear differential equation with constant coefficients O c. None of these O d. linear second order differential equation with constant coefficients O e. homogenous equation with constant coefficientsThe 5 vectors: 10cm at 72k degrees, k= 0, 1, 2, 3, 4 encompass the sides of a regular pentagon. Determine the magnitude of the vector cross-product: 2.5{(10/ at 144 deg) x (10/at 216 deg)}. Select one: O a. 237.7 O b. 198.1 O c. None of these O d. 165.1 O e. 285.2If the sum of the squares of 10 numbers is 645 and their standard deviation is 2.887, find their arithmetic mean. Select one: O a. None of these O b. 9.5 O c. 7.5 O d. 8.5 O e. 6.5Find the Laplace transform of (sin t) / t Select one: O a. arctan (1/s) O b. arcsin (S) O c. None of these O d. arc sec (S) O e. cot (S)