4. Find the Taylor series ofat x=1.（15%）

一、英譯中：請將下面這段英文譯成正確、流暢的中文（30 分） The global issues that we face today can seem overwhelming—too much for any person, any one organization, or any one government to tackle. As we size up the global challenges we face—from advancing gender equality to eliminating poverty—it’s crucial to recognize that these issues do not exist in silos. For instance, progress we have made on issues related to health and security are exacerbated by climate change. Only by looking at these challenges holistically, can we have a better chance at making progress on a range of issues. Facing different problems in human existence, what can humans accomplish collectively? That’s where the Sustainable Development Goals come in, a framework designed by the United Nations for peace and prosperity for both people and the planet.

1. Find the value of the limit .（10%）

2. Evaluate the integral ∫ ex (2x+1) dx  .（10%）

3. Find an equation of the tangent line of the curve x3+xy+2x2+y3+1=0 at （-2,1）. （10%）

5. Evaluate ∫∫D xy2 ds where D is the triangle with vertices （0,0）, （0,2） and （1,0）. （15%）

(1)

(2)

7. Find the outward flux of the vector field （8%） across the surface of the region that is enclosed by the circular cylinder  x2+y2=9 and the planes z=0 and z=2 .

（a） C does not enclose the origin.

（b） C enclose the origin.