Find the approximate value. If the approximate value is equal to the exact value, is it written as approximately equal to or equal to If 5 retains two decimal places, is it written as approximately equal to or equal to 5.00

Find the approximate value. If the approximate value is equal to the exact value, is it written as approximately equal to or equal to If 5 retains two decimal places, is it written as approximately equal to or equal to 5.00

Of course it's equal. If it's exactly equal, it doesn't have to be about equal

Mathematical emperor, help, use calculus to find the approximate value, 0.0001 power of E, first aid

one

Calculate the approximate value: the third power of (1.02) under the heel sign + (1.97) Let f (x, y) = the third power of X under the heel sign + the third power of Y, and then take the derivatives of X and Y respectively, Let x = 1, y = 2, the change of x = 0.02, and the change of y = -0.03 (why can this be done?) So f (1,2) = the third power of 1 under the heel sign + the third power of 2 = 3, The change of F = the derivative of FX times the change of X + the derivative of FY times the change of Y So the original formula is about equal to the change of F (1,2) + F (why?)

Let f (x, y) = the third power of X + the third power of Y under the following sign, and then take the derivatives of X and Y respectively, let x = 1, y = 2, the change of x = 0.02, and the change of y = -0.03 (why can it be so?) 1.02 = X+ Δ x1.97 = y + Δ YX = 1, y = 2, so Δ x=0.02, Δ Y = -0.03, so f (1,2) = the third power of 1 under the heel sign

What is the approximate value of the third power of 1.002?

The third power of 1.002
=The third power of (1 + 0.002)
=1 + 0.002 * 3 + 0.002 to the second power * 3 + 0.002 to the third power
Approximately equal to 1.006

Let f (x) = the x-power-1 of E, what is the approximate value of F (0.1) obtained by calculus?

Linearization by differential
Take x = 0
f(0)=1-1=0
∵f'(x)=e^x
f(x)≈f(a)+f'(a)(x-a)
∴f(0.1)=f(0)+f'(0)(0.1)=0.1

Use calculus to calculate the approximate value of 10 ^ 2.03 Wrong number. It's differential

Approximately 100 + 0.03 · 100 · ln10 = 100 + 3ln10