∫(2eˣ - 3√x)dx
The integral ∫(2eˣ - 3√x) dx can be solved by applying the standard rules of integration. For the first term, ∫2eˣ dx, we use the rule that the integral of ______ __________ __________ ______ _________ __________ ___ ___ ____ __________ __________.
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(a) Which of the following sets are finite, and which are infinite?
(i) The set of points on the circumference of a circle.
(ii) ]0, 1[
(iii) [-1, 1]
(iv) {1, 2, ..., 100}
(b) If A = {1, 2, 3}, B = {2, 3, 4, 5}, and C = {1}, determine A ∪ B ∪ C and also verify
A ∪ B ∪ C = (A ∪ B) ∪ C = A ∪ (B ∪ C)
(a) If A = 
then show that
(i) 1/2 (A + A') is symmetric, and
(ii) 1/2 (A - A') is skew symmetric.
A number is chosen at random from the first 40 natural numbers. Calculate the probability that the selected is divisible by 5 or 7.
(a) Define Error and their types in quantitative chemical analysis.
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(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)
(ii) 3x/√(5+2x²)
√(d³y/dx³) = dy/dx + x⁴
In an iron determination from the same amount of sample, the five replicate results were obtained: 20.1, 19.6, 20.0 and 19.9 and 20.4 mg iron.
Calculate the standard deviation, variance, standard deviation of mean, coefficient of variation and relative standard deviation in ppm of the given data.