Example 4 Video Example
Prove that -(sinh-l(x)) =
dx
√1+x²
Solution 1
Let y
sinh (x). Then sinh(y) = x. If we differentiate this equation implicitly with respect to x, we get
1.
dx
Since cosh?() - sinh?(y) = 1 and cosh(y) 2 0, we have cosh(y) - 1 + sinh?(y), so
1
dy
dx
1
cosh(y)
V1 + sinh?v)
Solution 2
we have
From the equation sinh-+(x) = \n(x + V x2 + 1).
-(sinh 'x) - 4 n(x + 2 + 1)-- --4(x + x + 1)
dx
- ** V*2+1 ( + vota)-
√²+1+x
1+1
+ 1
1

4.6875 pounds

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: