Determine the domain and range of the function

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Reference no: EM132353732

Introduction To Mathematical Modelling Assignment Questions -

Q1. Determine if the following functions are even, odd or neither.

(i) f(x) = (x³-2x)/(5x⁴-x²)

(ii) f(x) = sin((x⁶-2x²)/(x⁴+2x²))

Q2. For the function y = f(x) = |2x + 3|,

(i) Determine the domain and range of the function.

(ii) Clearly sketch the function showing important points, i.e. intercepts.

(iii) Find a restriction of the domain such that the function is one-to-one.

Q3. Evaluate the following limits:

(i) lim_x→-3(x²-3x-18)/(x²+8x+15)

(ii) lim_x→∞(6x³-4x+7)/(5-2x²-3x³)

Q4. Find the derivative of the following functions:

(i) y = (xe^x + sinx)⁷

(ii) y = (x³ + x)sin^-1x

Q5. Using implicit differentiation, determine dy/dx if

sin(yx) = y²

Q6. Using logarithmic differentiation, determine dy/dx if

y = (x⁴-3x³+5)^1/3/(x³-7x²)^2/5

Q7. Is there a number b such that lim_x→1(x²+2bx-b-2)/(x²-4x+3) exists? If so, find the value of b and the value of limit.

Q8. For the curve x² + xy + y² = 6, find the points where tangent is parallel to the (a) x-axis; (b) y-axis.

Reference no: EM132353732

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