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1. Write down the domain and range of each function. 3%

1.1 ^y ^{2 x} 1.2  

2

y x 1.3 ( 1)2

1

  y x

2. Write the answers of each question. 3%

2.1 )

4 7 )(8

2 1 ( 1

lim ₂

2 2 2

v v v v v

v









 2.2

x x

x

limln



 2.3 ⁿ

n n

x) 1 ( lim 





3. According to the equation^{y 4x3x4}, (1) write down the interval where y is increasing and is decreasing; (2) write down the interval where y is concave up and is concave down; (3) write down all of its local extreme points and inflection points. 14%

4. Find the derivatives of y. (Find dy/dx.)24%

4.1 y x x

2 5 3

1

2 

 4.2 y ln(3xe^x) 4.3

1

 _x^x e y e

4.4 ⁴ ))³

(12 tan 1

( x

y   4.5 x²yxy² 6 4.6 y log₂xlog₄ x 4.7 ^{y  xsinx} 4.8 y tan^1 x²1csc^1x, x1

5. Evaluate the integrals. 40%

5.1 dt

t t t



t ^{2 5.2}

^

^{sin2xdx 5.3 3y 73y2dy}

5.4



0^ln2xe^x2cos(e^x2)dx 5.5



0²

cos sin 7



dt

t t 5.6



_x(ln⁴_x)^2dx

5.7



² _

-2 1 (sin )2

cos

 2

 



 d

5.8



1²xlnxdx 5.9



^{(x2 5x)exdx}

5.10



_x²_^x₅^_x⁴_6^dx

6. Find the areas of the shaded regions graphed below. 6%

7. The region bounded by the curve ^{y x21} and the line ^{y x3} is revolved about the x-axis to generate a solid. Find the volume of the solid. 10%