Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We need to evaluate the definite integral $K = \int_0^1 (x^2 + 1)^7 x \, dx$.

Definite IntegralIntegration by SubstitutionPower Rule of Integration

We are asked to find the limit of the function $\frac{e^x - e^{-x}}{2e^x}$ as $x$ approaches $0$. Th...

LimitsExponential FunctionsCalculus

Given the function $y = x^3 - x$ with graph C. a. Show that A(-1, 0) is an intersection point betwee...

CalculusDerivativesTangent LinesIntersection of CurvesQuadratic EquationsVieta's Formulas

The problem asks us to differentiate the function $f(x) = \frac{x^3 - 2x^2 + x - 3}{x}$ with respect...

DifferentiationCalculusPower RuleFunctions

We are asked to solve several math problems, including finding limits, probabilities, integrals, com...

LimitsProbabilityIntegrationCalculusDefinite IntegralsIndefinite Integrals

We are asked to solve the following problems from the image: a. $\lim_{x \to 0} (2e^x - xe^x + 2e^0 ...

LimitsCalculusTrigonometryExponentials

We are asked to differentiate two functions with respect to $x$. a) $f(x) = (3x^2)(x^2)(x^2 + 2x + 1...

DifferentiationCalculusPower RuleQuotient Rule

We are asked to solve two limit problems. a) $\lim_{x\to 3} \frac{1}{x-3}$ b) $\lim_{x\to 0} \frac{2...

LimitsCalculusLimits of Rational Functions

We are presented with several math problems to solve, including limits, probabilities, integrals, co...

LimitsCalculusAsymptotes

The image presents several math problems, including calculations of definite integrals, complex numb...

Definite IntegralsIntegrationSubstitutionCalculus

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