We can compare the estimates from the linear approximations above, then we can find that the tangent line approximation gives good estimates whenxis close to 1.
When I studied at primary school,I learned the ways to calculate the surface area and the volume of rectangle,square and cylinder,and the volume of cone.I knew rectangle and square are measured by the unite square ;we...When I studied at primary school,I learned the ways to calculate the surface area and the volume of rectangle,square and cylinder,and the volume of cone.I knew rectangle and square are measured by the unite square ;we calculate the volume of the cylinder by cutting cylinder into pieces and putting the pieces together approximates the rectan-展开更多
We used tables and graphs by using graphing-calculator to guess values of limits,however,we found methods we used don’t always lead to the correct answer.Theproperties of limits have been found.It iseasy to believe t...We used tables and graphs by using graphing-calculator to guess values of limits,however,we found methods we used don’t always lead to the correct answer.Theproperties of limits have been found.It iseasy to believe they are true.For example,iff(x)is close to Land g(x)is close to M,itis reasonable to get the result that f(x)展开更多
If a function f(x) is differentiable,then the linear approximation of f(x) at a is f(x)≈f(a)+f′(a)(x-a),while the value of x close to a.The equation L(x)=f(a)+f′(a)(x-a) is called the linearization of f(x) at a.
High School Attached CNU(1 00048) Yuxue Liang Last time we have done Example 1,there is not only one function in fact,b ecause x-axis is the function y=0.Example 1:Find the area
It is easy to find the area of a rectangle or a triangle,even a polygon,which it is found by dividing it into triangles then summing the areas of the triangles.How to find the area of the region R that is bounded
The precise definition of a limit is represented in graphically,numerically,analytically and verbally by using algebraic way.The intuitive definition of a limit is given as "the limit of f(x),as x approaches a,eq...The precise definition of a limit is represented in graphically,numerically,analytically and verbally by using algebraic way.The intuitive definition of a limit is given as "the limit of f(x),as x approaches a,equals L ",and we write lim x→af(x)=L.But the more questions will be asked if you think it broadly."Is the definition of the limit of function vague?" "How should be x close to a presented algebraically?" "How should be f(x) gets closer and closer to L presented algebraically?" "How close to a does x展开更多
In mathematics and computational science,the Euler’s Method,named after Leonhard Euler,is a first-order numerical procedure for solving ordinary differential equations (ODEs)
Example 2:At time t≥0,aparticle moving in the xy-plane has vector given by V(t)=[X(t),Y(t)]=[t2,5t].What is the acceleration vector of the particle at timet=3? Solution:From the condition is given,we know X(t)=t2 and...Example 2:At time t≥0,aparticle moving in the xy-plane has vector given by V(t)=[X(t),Y(t)]=[t2,5t].What is the acceleration vector of the particle at timet=3? Solution:From the condition is given,we know X(t)=t2 and Y(t)=5t.展开更多
Do you remember the composite function which is composed of two functions,we’ve learned.Such as f(x)=g(φ(x))withφ(x)is called inside function and g(x)is called outside function.You
We have previously met the limits with the indeterminate form 0 0 .For example,in the rational functions,we can cancel common factors as the one shown below.
Example 2: Givenf′(x)=3/xand starting at point (1, 0). The next two points of the Euler line using△x=0.5. By using Euler s method find the y-values with three steps.
1. Limits at infinityLet’s begin by investigating the behavior of the function f(x) = 1/x as x becomes large. You can use the graphing - calculator(TI - 84 Pluse)to set the table numerically and have the graph.As x b...1. Limits at infinityLet’s begin by investigating the behavior of the function f(x) = 1/x as x becomes large. You can use the graphing - calculator(TI - 84 Pluse)to set the table numerically and have the graph.As x becomes larger and larger you can see展开更多
文摘We can compare the estimates from the linear approximations above, then we can find that the tangent line approximation gives good estimates whenxis close to 1.
文摘When I studied at primary school,I learned the ways to calculate the surface area and the volume of rectangle,square and cylinder,and the volume of cone.I knew rectangle and square are measured by the unite square ;we calculate the volume of the cylinder by cutting cylinder into pieces and putting the pieces together approximates the rectan-
文摘We used tables and graphs by using graphing-calculator to guess values of limits,however,we found methods we used don’t always lead to the correct answer.Theproperties of limits have been found.It iseasy to believe they are true.For example,iff(x)is close to Land g(x)is close to M,itis reasonable to get the result that f(x)
文摘If a function f(x) is differentiable,then the linear approximation of f(x) at a is f(x)≈f(a)+f′(a)(x-a),while the value of x close to a.The equation L(x)=f(a)+f′(a)(x-a) is called the linearization of f(x) at a.
文摘High School Attached CNU(1 00048) Yuxue Liang Last time we have done Example 1,there is not only one function in fact,b ecause x-axis is the function y=0.Example 1:Find the area
文摘It is easy to find the area of a rectangle or a triangle,even a polygon,which it is found by dividing it into triangles then summing the areas of the triangles.How to find the area of the region R that is bounded
文摘The precise definition of a limit is represented in graphically,numerically,analytically and verbally by using algebraic way.The intuitive definition of a limit is given as "the limit of f(x),as x approaches a,equals L ",and we write lim x→af(x)=L.But the more questions will be asked if you think it broadly."Is the definition of the limit of function vague?" "How should be x close to a presented algebraically?" "How should be f(x) gets closer and closer to L presented algebraically?" "How close to a does x
文摘In mathematics and computational science,the Euler’s Method,named after Leonhard Euler,is a first-order numerical procedure for solving ordinary differential equations (ODEs)
文摘Example 2:At time t≥0,aparticle moving in the xy-plane has vector given by V(t)=[X(t),Y(t)]=[t2,5t].What is the acceleration vector of the particle at timet=3? Solution:From the condition is given,we know X(t)=t2 and Y(t)=5t.
文摘Do you remember the composite function which is composed of two functions,we’ve learned.Such as f(x)=g(φ(x))withφ(x)is called inside function and g(x)is called outside function.You
文摘We have previously met the limits with the indeterminate form 0 0 .For example,in the rational functions,we can cancel common factors as the one shown below.
文摘Example 2: Givenf′(x)=3/xand starting at point (1, 0). The next two points of the Euler line using△x=0.5. By using Euler s method find the y-values with three steps.
文摘1. Limits at infinityLet’s begin by investigating the behavior of the function f(x) = 1/x as x becomes large. You can use the graphing - calculator(TI - 84 Pluse)to set the table numerically and have the graph.As x becomes larger and larger you can see
