Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The image contains several math problems. I will solve problem "ក" (first problem). It asks to calcu...
LimitsCalculusExponential Functions
2025/5/20
The provided text contains several math problems. We will solve problem "I" which is an integral: $I...
IntegrationCalculusIntegration by PartsDefinite Integrals
2025/5/20
We are asked to solve three limit problems: a) $\lim_{x \to 0} (2e^{3x} - xe^x + 2e^x + 4)$ b) Find ...
LimitsCalculusExponential FunctionsTrigonometric Functions
2025/5/20
We need to evaluate two limits: a) $\lim_{x\to 3} \frac{1}{x-3}$ b) $\lim_{x\to 0} \frac{2x+2}{3x+5}...
LimitsCalculusContinuity
2025/5/20
The problem is to find the limit of the function $\frac{1}{x-3}$ as $x$ approaches 3. We need to ev...
LimitsFunctionsCalculusDivergence
2025/5/20
The problem asks us to evaluate two integrals and two limits. (a) $\int \frac{x^2}{2} dx$ (b) $\int ...
IntegrationLimitsCalculus
2025/5/20
We need to evaluate two indefinite integrals. a) $\int \frac{x^2}{2} dx$ c) $\int \frac{1}{(x + \fra...
IntegrationIndefinite IntegralsPower RulePartial FractionsCalculus
2025/5/20
The problem asks to evaluate two indefinite integrals: a) $\int \frac{x^2}{2} dx$ b) $\int \frac{x}{...
Indefinite IntegralsIntegrationPower RuleU-SubstitutionAlgebraic Manipulation
2025/5/20
We need to differentiate the function $y = 3x^2 + 2x + 5$ from first principles.
DifferentiationFirst PrinciplesLimitsCalculus
2025/5/20
The problem consists of two parts. The first part asks to differentiate $y = 3x^2 + 2x + 5$ from fir...
DifferentiationCalculusFirst PrinciplesQuotient RulePower Rule
2025/5/20