4. Find the exact value of each expression.(每小題4分)【題組】(a) f(4)=?, where f(x) = In
【題組】(b) sin=?
5. The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick,use dif
6.z = f(x,y)=x2y3-4y2【題組】(a)Find ∇f(x,y)the gradient of f(x,y).(5分)
【題組】(b)Find dz the total differential of z.(5分)
【題組】(c) Evaluate Duf(1,2) the directional derivative of f(x,y) at (1,2) in thedirection of the unit
7. Evaluate【題組】(a) .(5分)
【題組】(b), where R is the triangular region with vertices (0,0), (4,4)and (6,0). (5分)
【題組】(b), k is a constant and k>0
2. Find the derivative of the function.(每小題 5%)【題組】(a) g(x) =sin3(cosx)
【題組】 (c)
【題組】(d) f(t)=(2t-1)t-2
3. Evaluate the definite integral.(每小題5%)sin' x -cos? x 【題組】(a)
5.計算【題組】(a)(5%)
4.(10%) Give the statements of the First and Second Fundamental Theorem of Calculus.(敘述微積分第一及第二基本定理:
【題組】(b)(5%).
【題組】(c)(5%)
【題組】(d)(5%)
6.計算【題組】(a)sin-1(sin(1.6))(5%)
【題組】(b)(5%)
7. Find the interval of convergence for the power series (7%)
8. Find a power series representation forand specify the radius ofconvergence.(8%)
4. Let. Find f(7)(0). (10%)
5. Letg (x)be the inverse function off(x ) =x ln x forx ≥ 1. Find. (10%)
2. (16%) Find the limit if it exists【題組】(1)