Geometric thinking

Geometric thinking affects success in learning geometry. Geometry is studied from elementary school to university level. Therefore, in higher education and basic education, it is necessary to carry out a systematic review in order to obtain tips for improving geometric thinking skills.

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In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval. In lecture Mathematics 53 - Lecture 1.5, you will learn: The intermediate value theorem, the squeeze theorem, limits and continuity of trigonometric functions.

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The main contents of this chapter include all of the following: Hyperbolic functions, identities involving hyperbolic functions, derivatives of hyperbolic functions, integrals of hyperbolic functions, inverse hyperbolic functions, derivatives of inverse hyperbolic functions, integrals yielding the inverse hyperbolic functions.

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The main contents of this chapter include all of the following: Limits at infinity, the formal definition, proving using the definition. Inviting you refer.

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Lecture provides knowledge of the continuity of functions. The main contents of this chapter include all of the following: Continuity of functions, continuity on an interval. Inviting you refer.

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Lecture provides knowledge of the integrals yielding logarithmic and exponential functions. This chapter presents the following content: Integrals of f(x) = 1/x and of the other circular functions, integrals of exponential functions, the natural logarithmic function: A rigorous approach.

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Lecture 1 - Addition and subtraction of natural numbers. In this lecture student teachers will be able to: Increase their mathematical content knowledge for numbers and operations, algebra and algebraic thinking, geometry and geometric measurement, and Information handling for teaching in elementary grades; increase their confidence, competence, interest, and enthusiasm for mathematics by exploring and doing mathematics; deepen an understanding of how children learn mathematics;…

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After studying this chapter you will be able to: Understand multiplication and division, know various models for arithmetic operations (multiplication, and division) with natural numbers, apply multiplication and division to solve word problems.

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Lecture provides knowledge of the one-sided limits and infinite limits. In this chapter, the following content will be discussed: One-sided limits (continuation), infinite limits. Inviting you refer.

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The main contents of this chapter include all of the following: Functions, basic types of functions, constructing a table of signs, operations on functions, piecewise-defined functions, functions as mathematical models.

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Lecture General mathematics - Lecture 8: Lecture General mathematics: Lecture 8. Lecture provides knowledge of the slopes and the derivative - Differentiation rules. This chapter presents the following content: The tangent line, definition of the derivative, differentiability, differentiation rules, derivatives of trigonometric functions.

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Lecture 9 - Patterns as fundamental to understand algebra. After studying this chapter you will be able to understand: Identify the number pattern involving different operations on number and repeat the sequence of number accordingly, understand the number pattern given and guess the missing numbers.

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Lecture 11 - Variables and coordinates. After studying this chapter you will be able to understand: To understand the cartesian coordinate system, to plot ordered pairs (points) on the cartesian coordinate system.

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Lecture 12 - Liner equations and graph of liner equations. After studying this chapter you will be able to understand: To understand the linear equations. to plot linear equations on the cartesian coordinate system.

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Lecture 13 - Slope of a linear equation. After studying this chapter you will be able to understand: Understand slope and its types, form the linear equations involving slopes of different situations.

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The main contents of this chapter include all of the following: Inverse circular functions, derivatives of inverse circular functions, integrals yielding the inverse circular functions.

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This chapter presents the following content: Mean value theorem for integrals, the first fundamental theorem of calculus, the second fundamental theorem of calculus.

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The main contents of this chapter include all of the following: Volumes of solids of revolution: Disk or washer method, volumes of solids of revolution: Cylindrical shell method, other examples: volumes of solids of revolution.

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Lecture provides knowledge of the continuity of functions. The main contents of this chapter include all of the following: Continuity of functions, continuity on an interval. Inviting you refer.

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The main contents of this chapter include all of the following: Definitions and examples, absolute extrema of functions on closed and bounded intervals, absolute extrema of functions with one relative extremum, other cases: using limits.

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