2026知到答案 微积分（Calculus）（华南理工大学） 最新智慧树满分章节测试答案
第一章 单元测试
1、单选题：
What is the correct interpretation of the limit expression 
?
选项：
A:The function f(x) is equal to 2 when x equals 1.
B:The function f(x) is continuous at x = 1 and has a value of 2.
C:The function f(x) gets infinitely close to 2 as x approaches 1, but never reaches it.
D:The function f(x) approaches 2 as x approaches 1, regardless of whether f(1) is defined.
答案: 【The function f(x) approaches 2 as x approaches 1, regardless of whether f(1) is defined.】
2、多选题：
Which of the following statements correctly describe the application of the squeeze theorem in evaluating trigonometric limits?
选项：
A:The squeeze theorem is applicable only to polynomial functions and cannot be used for trigonometric limits.
B:
The squeeze theorem can be applied to prove 
by considering areas in the unit circle.
C:
The squeeze theorem is used to show that 
by bounding the function between 
and 
.
D:
The squeeze theorem can directly evaluate limits like 
without requiring any algebraic manipulation.
E:To apply the squeeze theorem, one must find two functions that bound the original function and have the same limit at the point of interest.
答案: 【
The squeeze theorem can be applied to prove by considering areas in the unit circle.
;
The squeeze theorem is used to show that by bounding the function between and .
;
To apply the squeeze theorem, one must find two functions that bound the original function and have the same limit at the point of interest.】
3、判断题：
The Squeeze theorem is only applicable to proving the limit 
when 
is greater than zero, and cannot be extended to cases where 
is less than zero.
选项：
A:错
B:对
答案: 【错】
4、单选题：
Which of the following statements correctly describes the behavior of the function 
as 
approaches 1 from the right?
选项：
A:The limit approaches negative infinity, indicating no asymptote.
B:The limit approaches infinity, indicating a vertical asymptote at x = 1.
C:The limit approaches 0, indicating a removable discontinuity.
D:The limit approaches 2, indicating a horizontal asymptote at y = 2.
答案: 【The limit approaches infinity, indicating a vertical asymptote at x = 1.】
5、判断题：
A function's limit at infinity describes its behavior as the input grows without bound, while an infinite limit describes unbounded behavior near a finite point.
选项：
A:对
B:错
答案: 【对】
6、判断题：
A function f is continuous at point c if and only if the limit of f(x) as x approaches c exists, f(c) exists, and the limit equals f(c).
选项：
A:对
B:错
答案: 【对】
第二章 单元测试
1、判断题：
函数的连续性和可微性之间是否存在直接的联系？
选项：
A:错
B:对
答案: 【对】
2、单选题：
Which of the following expressions correctly represents the derivative of a function 
at point 
using the limit definition?
选项：
A:
B:f'(x) = lim_{h to 0} frac{f(x + h) - f(x)}{h}
C:
D:
答案: 【
】
3、判断题：
The derivative of a constant function 
is always zero, regardless of the value of 
.
选项：
A:对
B:错
答案: 【对】
4、多选题：
Which of the following statements correctly apply the chain rule to find derivatives of composite functions?
选项：
A:
The chain rule states that 
, but this only applies when both 
and 
are linear functions.
B:
When differentiating 
, the chain rule is not applicable because the exponent is too large.
C:
For 
, the derivative is 
by applying the chain rule to the composition of three functions: 
, 
, and 
.
D:
For 
, the derivative is 
by sequentially differentiating the composition layers: 
, 
, and 
.
E:
The derivative of 
can be found by rewriting it as 
where 
, then applying 
.
答案: 【
For , the derivative is by applying the chain rule to the composition of three functions: , , and .
;
For , the derivative is by sequentially differentiating the composition layers: , , and .
;
The derivative of can be found by rewriting it as where , then applying .
】
5、单选题：
What is the mathematical expression of the chain rule for the composition of two differentiable functions y = f(u) and u = g(x)?
选项：
A:
B:
C:
D:
答案: 【
】
6、判断题：
The chain rule states that the derivative of a composite function 
is given by 
, where 
.
选项：
A:对
B:错
答案: 【对】
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