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Exponential and logarithmic functions

Growth and decay, the number e, log rules, and change of base.

bˣ grows by the same factor for each unit of x; its inverse log_b x asks which exponent produces x. The rules log(ab) = log a + log b and log aᵏ = k log a are the exponent rules read backwards. Picture it: the exponential curve and its log are mirror images across y = x. Think it: e is the base whose growth rate equals its value, which is why calculus prefers it.

Ишлатилган мисол · y = e^x

Algebra · Functions

Graph and analyse e^(x)

y = e^{x}

Қадамма-қадам

  1. e^{x}

    An expression in x. Here is what it does.

  2. \frac{d}{dx} = e^{x}

    Derivative (slope).

Жавобни кўрсатиш
e^{x}

Энди сизлар Мавзуни танланг, ёзинг ёки ўзингиз чизинг. Ҳар бир қадам, расм, жавоб сиз сўрагунча яширин.

Ўзингиз ишлашда давом этинг

Бепул ҳисоб ҳар бир дарсга ёзув қўшиб беради, сиз тугатган нарсалар ва ҳал қилинган масалалар бир жойда қайд этилади ва сиз бу саҳифа ҳақида устоздан сўрашингиз мумкин. Математика ўзида очиқ бўлиб, унга кириш ёки киришни истамаган ҳар кимга очиқ.

Ройхатдан ўтиш Кириш

Бу ерда қўлланилган белгилар

Барча белгилар учун тўлиқ таъриф, сурат ва ҳар бир ҳарфнинг маъносини кўриш учун белгини босинг.

Қандай: Exponential and logarithmic functions

  1. An expression in x. Here is what it does.
  2. Derivative (slope).

Одамлар сўрайдиган саволлар

What is a function, really?

A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.

Why do we need complex numbers?

Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.

Кўпроқ Precalculus

Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremConic sectionsVectorsPolynomial division and the remainder theoremParametric equations and polar coordinates