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An infinitesimal is a number that is infinitely close to zero, but not zero, for example, n->+, (1, 10) n=zero)1 This is an infinitesimal and you say it is not equal to zero, right, but infinitely close to zero, take any of the values cannot be closer to 0 than it (this is also the definition of the limit in the academic world, than all numbers ( ) are closer to a certain value, then the limit is considered to be this value) The limit of the function is when the function approaches a certain value (such as x0) (at x0). 'Nearby'The value of the function also approaches the so-called existence of an e in the definition of a value, which is taken as x0'Nearby'This geographical location understands the definition of the limit, and it is no problem to understand the infinitesimite, in fact, it is infinitely close to 0, and the infinitesimal plus a number, for example, a is equivalent to a number that is infinitely close to a, but not a, how to understand it, you see, when the chestnut n->+, a+(1, 10) n=a+ is infinitely close to a, so the infinitesimal addition, subtraction, and subtraction are completely fine, and the final problem of learning ideas, higher mathematics, is actually calculus, and the first chapter talks about the limit In fact, it is to pave the way for the back, and the back is the main content, if you don't understand the limit, there is no way to understand the back content, including the unary function, the differential, the integral, the multivariate function, the differential, the integral, the differential, the equation, the series, etc., these seven things, learn the calculus, and get started.

<> understand the definition of the limit of the function and use the definition proficiently, then you can understand the proof of theorem 2 and theorem 3.

Summary. 1): 1 x in f(x) tends to an infinite mass, and the cos(1 x) range is bounded by |cos(1/x)|<1, when cos(1 x)=0, f(x)=1, when cos(1 x)=1, f(x)=1 x, when x approaches 0, it is a larger quantity, so f(x) is a function that constantly changes between positive and negative infinity, and constantly crosses the 0 point; (2)：

In the broad definition of limit, the limit can be infinity, but in the narrow definition, when the limit is infinite, the limit is said to be non-existent, and generally in high school, it is defined in the narrow sense; (3): infinitesimal quantities approach negative infinity; (4): When x is not equal to 0, multiply up and down (1+bx)?

1. The numerator becomes bx, and the x is removed after reduction, f(x)=b ((1+bx)?+1), substituting x=0, b=6;(5): The definition of the limit determines that the limit at a certain point is determined by the function near the point, and has nothing to do with the function value of the point.

When f(x) is a continuous function, the point limit is equal to the point limit, which is also the definition of a continuous function.

Write about the detailed process.

1): 1 x in f(x) tends to an infinite mass, and the cos(1 x) range is bounded by |cos(1/x)|<1, when cos(1 x)=0, f(x)=0, when cos(1 x)=1, f(x)=1 x, when x approaches 0, it is a larger quantity, so f(x) is a function that changes between positive and negative car rentals, and constantly crosses 0 points; Zhifan Da (2): In the broad definition of limit, the limit can be infinite, but in the narrow definition, when the limit is infinite, the limit is said to be non-existent, and it is generally defined in the narrow sense when I am in high school; (3)：

Infinitesimal quantities approach negative infinity; (4): When x is not equal to 0, multiply up and down (1+bx)?+1, the numerator becomes vertical bx, and the x is removed after reduction, f(x)=b ((1+bx)?

+1), substituting x=0, b=6;(5): The definition of the limit determines that the limit at a certain point is determined by the function near the point, and has nothing to do with the function value of the point. When f(x) is a continuous function, the point limit is equal to the point limit, which is also the definition of a continuous function.

Hello, this question uses the chain rule of derivatives.

Namely. Dy dx = (Dy dt)(dt dx) Specifically, y and x are respectively derived from t, y is placed on the numerator for x, and x is placed on the denominator for t, so that an expression 1 about t can be obtained, and then through the given parameter expression, t is expressed with x, which can be brought into the above calculation of expression 1.

Take question 8 as an example.

dy/dt=1-2t

dx/dt=-2t

Expression 1 is 1-2t -2t

Then the relationship between x and t gives t=(1-x).

Just bring in Expression 1. Hope!

It is possible to use the commutation method. Let t=(x-1) x,f(t)=1 t, i.e., f(x)=1 x,x≠0,1

It can be seen directly: f(x) = 1 x

Alternatively, you can make u = x-1) x, 1 u = x (x-1) =f(u) =1 u

It seems that the exchange of yuan directly gets f(x)=1 x? Maybe it's right to mark x≠0 and 1?

Question 1 c, the product of the infinitesimal quantity and the bounded quantity is still an infinitesimal quantity.

In the second question, choose d,x lead wisdom this 1, y bi type.

Excuse me to send a high number question** or type over, thank you.

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<> look at the figure, the unit vector is a vector with a length of 1, and the other two direction angles are the same, then the point is on the plane of the perpendicular bisector x0y, and then according to the angle with the z-axis is 6 and the length is 1, you can determine the four points, the coordinates can be found with trigonometric functions, don't understand and ask again.

Because it is a space vector and a unit vector, it can be expressed as.

cosα, cosβ, cosγ}

then the sum of squares of the cosine.

cos) 2+(cos) 2+(cos) 2=1 while cos = cos 6= 3 2

cosα=cosβ

So cos = cos = 2 4

So the p-point coordinates are.