lim x->0 sinx/x = 1 | H.A.: compare degrees | V.A.: denom = 0 | Continuous if: f(a), lim, equal
DERIVATIVES: (x^n)'=nx^(n-1), (e^x)'=e^x, (a^x)'=a^x ln a, (lnx)'=1/x | (uv)'=u'v+uv', (u/v)'=(u'v-uv')/v^2 |chain: (f(g(x)))'=f'(g(x))g'(x)
TRIG DERIVATIVES: (sin)'=cos, (cos)'=-sin, (tan)'=sec^2 | (sec)'=sec·tan, (csc)'=-csc·cot, (cot)'=-csc^2
CRITICAL POINTS:f'=0 or DNE ⇒ crit pt | f'>0 inc | f'<0 dec | f''>0 conc up | f''<0 conc down | inflec = f'' signchange
INTEGRATION: ∫x^
Shows concepts only: classes, attributes, associations, multiplicities.
No methods, no UI, no controllers.
Purpose: understand the real-world objects.
Actor ↔ System interaction.
Verb+noun name.
Format: Actor step vs System step.
Use cases → sequence diagrams → class diagrams.
🔵 UML CLASS DIAGRAM (Module 7)
Class: name, attributes, methods.
Association: line with multiplicity (1, 0..1, , 1..).
Inheritance: open triangle
१) वर्ण का मतलब बताकर उसका वर्गीकरण स्पष्ट कीजिए।
उत्तर:
वर्ण का अर्थ : वर्ण उस मूल ध्वनि को कहते हैं, जिसके और टुकड़े या खंड नहीं किए जा सकते। यह भाषा की सबसे छोटी इकाई है। उदाहरण के लिए— 'अ', 'क', 'ख',
Q1. Differentiate visual and non-visual programming language.
Visual programming languages allow developers to create programs using graphical elements like forms, buttons, and drag-and-drop tools. In a visual environment, the programmer focuses more on designing the interface and linking events rather than writing complex lines of code. Visual Basic (VB) is a good example, where you can create applications by placing controls on a form. These languages make development faster, easier, and more
1. If reflected/refracted rays never meet, the image is virtual because the rays only appear to meet when extended backward. This happens in plane & convex mirrors and in diverging lenses, or in converging lenses when the object is inside F.
2a. Refraction is the bending of light as it changes speed moving between media. 2b. Rules: (1) Low→high density = toward normal. (2) High→low density = away from normal. 2c. Higher optical density = higher refractive index. 2d. Symbol = n.
3a. Critical
B. Writing Essays
1. Essay on National Unity
National unity is the foundation of peace, progress, and stability in any nation. It is the feeling of togetherness, harmony, and mutual understanding among people belonging to different castes, religions, languages, and regions. In a country like Nepal, where people follow diverse traditions and lifestyles, national unity becomes even more important. Unity helps citizens work together for common goals, protects the nation’s identity, and strengthens...
1. Transmission Media
Transmission media refers to the physical or wireless pathways through which data travels from one device to another in a network. It plays a crucial role in determining the speed, quality, and reliability of communication. Transmission media is broadly classified into guided and unguided media. Guided media includes cables like twisted pair, coaxial cable, and optical fiber, where signals travel through a fixed physical path. Optical fiber offers the highest bandwidth and