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已知

a=0.33^{z}, b=\left(\frac{1}{\mathrm{e}}\right)^{e}

(e为自然对数的底数)

c=\tan 1

...

Mar 8, 2024

已知

a=0.33^{z}, b=\left(\frac{1}{\mathrm{e}}\right)^{e}

(e为自然对数的底数)

c=\tan 1

，比较

a, b, c

的大小（） A. a>b>c B. b>a>c C. c>a>b D. c>b>a

Generated Graph

Solution by Steps

step 2

Next, we look at

b = \left(\frac{1}{e}\right)^e

. This is a constant value and the asksia-ll calculator approximated it as

0.0659880358453125370767901875968464249385770482527964364024735415...

, which is less than 1

step 3

Lastly,

c = \tan(1)

, which is also a constant value. The asksia-ll calculator provided the approximation

1.5574077246549022305069748074583601730872507723815200383839466056...

, which is greater than 1

step 4

Since

c

is greater than 1,

b

is a positive number less than 1, and

a

is also less than 1 but variable, we can determine that

c

is the largest. Without knowing the exact value of

z

, we cannot compare

a

and

b

definitively. However, if

z

is positive,

a

will be less than

b

Key Concept

Comparing constant and variable expressions

Explanation

To compare the given expressions, we evaluate the constant values and consider the variable expression's behavior for positive values of

z

. Since

c

is greater than 1 and

b

is a positive fraction,

c

is the largest.

a

is dependent on

z

, but for positive

z

, it will be less than 1 and potentially less than

b