Define subjective, injective, and bijective functions with the examples.
_____ _____ ____ __________ ____ __________ ___ ____ _____ _______ _________ _________.
__________ ____ __________ ____ _____ _______ _____ _____ _____ _____ ____ ____.
_____ __________ _____ ________ ____ ___ __________.
_______ ________ _____ _______ _________ _______ ________ _____ __________ __________ _______.
____ _____ _______ ______ _______ _________ ______ _____.
__________ _________ _____ _______ _______ _________ __________ _______ ______ _______.
___ ___ __________ _______ ____ ____.
______ _______ ___ _____ ___.
______ ____ ___ ______ _______ __________ _________ ___.
____ _________ _______ __________ ________ ___.
_________ _______ ___ ___ _____ _________ ___ _______ _____ _____ ____.
____ __________ ______ ____ ________.
__________ ____.
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(a) Evaluate the following limit.
(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)
i) find its velocity and acceleration.
ii) find the distance covered by the particle in time t = 5 units
1.50 mol of PCl₅(g) is decomposes at room temperature to form PCl₃(g) and Cl₂(g). Determine their concentration at equilibrium, when K_c = 1.80.
Solve the following system of equations using Cramer's rule.
x + y - z = 6
3x - 2y + z = -5
x + 3y - 2z = 14
(a) Define Error and their types in quantitative chemical analysis.
(dy/dx)³ = √(1+(dy/dx)²)
Solve the following differential equation:
(1/y²) (dy/dt) = 1 - e⁻³ᵗ
(c) Show that the equation
(y - 2x³)dx = x(1 - xy)dy
becomes exact on multiplication by x⁻² and solve it.
Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2.