1 What is the equivalent infinitesimal of cosx 2?

1-(cosx) is equivalent to sin x. Equivalent infinitesimal is a type of infinitesimal.

At the same point, the limit of the ratio of these two infinitesimal is 1, and the two infinitesimal are said to be equivalent. An equivalent infinitesimal is also an infinitesimal of the same order. On the other hand, the equivalent infinitesimal can also be seen as Taylor's formula from zero to the first order.

1-(cosx) is equivalent to sin x. Equivalent infinitesimal

It is an infinitesimal kind.

Equivalent infinitesimal substitution is a common method for calculating the unshaped limit, which can simplify the problem of finding the limit.

When finding the limit, use the condition of the equivalent infinitesimal :

The limit value of the amount to be substituted is 0 when taking the limit;

The quantity to be substituted can be substituted as an element to be multiplied or divided, but not as an element of addition or subtraction.

1-(cosx)2 is equivalent to sin x

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His method converts 2sin(x 2 2) 2=x 4 2 using the doubling equation

<>cosx) 2 and cos(x 2) are two different functions.

Xie Xuan Song teased the answer to Zheng:

In the stove oak trigonometric function there is a leaky identity:

sin²x + cos²x = 1

So, 1 - cos x = sin x

When x 0, there is lim(sinx) x.

Then when x 0, lim(1-cos x) = lim(sin x) x

1-cosx is equal to x 2Equivalent infinitesimal

The details are as follows: because:

cos2a=1-2sin²a

1-cos2a=2sin²a

So: 1-cosx = 2sin (x 2) 2 (x 2) x 2 so 1-cosx is equal to x 2 equivalent to no grinding friend is poor and small.

Double-angle half-angle formula:sin ( 2α )2sinα ·cosαsin ( 3α )3sinα -4sin & sup3 ; 4sinα ·sin ( 60 + sin ( 60 -

sin ( 2 ) blind hand ( ( 1 - cos )2) is derived from the Taylor series:

sinx = e ix ) e ix ) 2i ) progression: sin x = x - x3 3! +x5 / 5!

1 ) k - 1 * x 2 k - 1 / 2k - 1 ) x <

Derivative: sinx ) cosx

cosx ) sinx

With the formula of double angle:

cos2a=1-2sin²a

1-cos2a=2sin²a

So: 1-cosx=2sin (x 2) 2 (x 2) x 2

So: 1-cosxEquivalent infinitesimal is x 2

Equivalent infinitesimal is a relation between infinitesimal and refers to: in the same independent variable.

If the limit of the ratio of the two infinitesimal selling beams is 1, then the two infinitesimal are said to be equivalent. The infinitesimal equivalence relation depicts that two infinitesimal approaches zero with equal velocity.

Equivalent infinitesimal middle beam exchange is a common method for calculating the limit of the unshaped slag circle, which can simplify the problem of finding the limit, and make it difficult to make it easy.

With the formula of double angle:

cos2a=1-2sin²a

1-cos2a=2sin²a

So: 1-cosx=2sin (x 2) 2 (x 2) x 2

So: the equivalent of 1-cosx is infinitesimal.

For Zen limb x 2.

The origin of the extremity.

Like all scientific methods of thought, limit thinking is also a social practice.

The brain is a product of abstract thinking. The idea of limits can be traced back to ancient times, for example, the circumcision of the motherland Liu Hui.

It is the application of a primitive and reliable "constantly approaching" limit idea based on the study of intuitive graphics.

The ancient Greeks' method of exhaustion also contained the idea of limits, but because of the Greeks' "fear of the 'infinite'", they avoided the obvious artificial "limits" and resorted to indirect proofs, the method of reduction.

to complete the relevant proof.

In the 16th century, the Dutch mathematician Kuanchai Stewin was examining the center of gravity of a triangle.

In the process, he improved the exhaustion method of the ancient Greeks, who boldly used the idea of limits to think about problems with the help of geometric intuition, and abandoned the proof of the method of imputation, so that he inadvertently "pointed out the direction of developing the limit method into a practical concept".

When x approaches 0, the ruler can reduce the function 1 - cos(x) to the form of none. According to Taylor's Gong 1 - cos(x) is the infinitesimal of x 2 2 equivalent to the vertical so that when x approaches 0, the valence of 1 - cos(x) is infinitesimal and the trap is large x.

When x approaches 0, the equivalent infinitesimal of 1-cosx can be expressed as x 2. This can be derived from the Taylor series. According to the Taylor series, the formula for cosx is:

cosx = 1 - x²/2!+x Samsara 4! -x⁶/6!+ Therefore, 1-cosx can be expressed as:

1 - cosx = x²/2! -x⁴/4! +x⁶/6!-When x approaches 0, the higher the power of the pre-fiber higher-order term, the smaller its contribution to the whole, so we can ignore the higher-order term and get:

1 - cosx ≈ x²/2

So, when x approaches 0, the equivalent infinitesimal of 1-cosx is x 2.

1-cosxEquivalent infinitesimal is x 2

With the formula of double angle:

cos2a=1-2sin²a

1-cos2a=2sin²a

So: 1-cosx=2sin (x 2) 2 (x 2) x 2So: the equivalent infinitesimal of 1-cosx is x 2

Introduction to the double angle formulaThe formula for double angles is a set of formulas commonly used in mathematical trigonometric functions, which are made by the trigonometric value of the angle.

Some transformation relations to represent the trigonometric values of their double angles2.

The formula for double angles includes the formula for sine double angles, cosine.

The formula for the double angle as well as the formula for the tangent double angle. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in calculations, and it is also widely used in engineering.

With the formula of double angle:cos2a=1-2sin²a

1-cos2a=2sin²a

So: 1-cosx=2sin (x 2) 2 (x 2) x 2So: 1-cosx's equivalent infinitesimal

is x 2Introduction to the double angle formulaThe double angle formula is a set of formulas that are often used in mathematical trigonometric functions, through the trigonometric value of the angle.

Some transformation relations to represent the value of the three-empty angle function of its double angle 2.

The doubling angle formula includes the sine doubling angle formula and cosine.

The formula for the double angle as well as the formula for the tangent double angle. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in calculations, and it is also widely used in engineering.

Hold on. The equivalent infinitesimal of 1-cosx is x with stupidity 2 As long as Tomono is when x 0 and (1-cosx) (x 2) stupid with 1, it means that the two are equivalent infinitesimals.

Excavate with the formula of double angle: cos2a=1-2sin a1-cos2a=2sin a so:1-cosx=2sin (x 2) 2 (x 2) blind call x 2 so:

The equivalent infinitesimal of 1-cosx is x 2

^x→0，1-cosx~x^2/2

Commonly used infinitesimal substitution formula:

When x 0, sinx x

tanx~x

arcsinx~x

arctanx~x

1-cosx~1/2x^2

a^x-1~xlna

e^x-1~x

ln(1+x)~x

1+bx)^a-1~abx

1+x)^1/n]-1~1/nx

loga(1+x)~x/lna