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Question: Determine the value of k for which the function f(x) = { kx + 1, x < 1; 2x - 3, x >= 1 } i..
Question: Determine the area under the curve y = e^x from x = 0 to x = 1.Options: e - 11e0Correct An..
Question: The function f(x) = x^3 - 6x^2 + 9x has how many local extrema?Options: 0123Correct Answer..
Question: The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:Options: 0123Correct Answer..
Question: If f(x) = ln(x) + x^2, then the function is increasing for:Options: x > 0x < 0x > 1x < 1Co..
Question: The minimum value of the function f(x) = x^4 - 8x^2 + 16 is:Options: 0124Correct Answer: 0..
Question: For the function f(x) = e^x - x^2, the point of inflection occurs at:Options: x = 0x = 1x ..
Question: The maximum value of the function f(x) = -x^2 + 4x + 1 occurs at:Options: x = 2x = 4x = 1x..
Question: If f(x) = sin(x) + cos(x), then the critical points in the interval [0, 2π] are:Options: π..
Question: The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:Options: y = ..
Question: If f(x) = x^3 - 3x^2 + 4, then the local maxima occurs at which point?Options: x = 0x = 1x..
Question: Evaluate the integral ∫(0 to 1) (x^3 + 2x^2)dx.Options: 1/41/31/21Correct Answer: 1/3Solut..
Question: If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?Options: {(1,1), (2,2), (3,3)}{(1,2), (2..
Question: If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?Options:..
Question: From a set of 8 different books, how many ways can you choose 3 books?Options: 56842870Cor..
Question: How many ways can 3 red, 2 blue, and 1 green balls be arranged in a row?Options: 601203090..
Question: In how many ways can 6 different objects be selected and arranged in a line?Options: 72060..
Question: What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?Options: 901..
Question: In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th t..
Question: What is the 7th term of the sequence defined by a_n = 2^n + 3^n?Options: 2187243256729Corr..
Question: If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what ..
Question: In an arithmetic series, if the first term is 5 and the last term is 45, and there are 10 ..
Question: Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.Options: 320302290310Correct..
Question: If the sum of the first n terms of a geometric series is 81, and the first term is 3, what..
Question: The roots of the equation 5x^2 - 20x + 15 = 0 are:Options: 1234Correct Answer: 2Solution: ..
Question: For the quadratic equation x^2 + 4x + k = 0 to have no real roots, k must be:Options: 0123..
Question: The equation x^2 - 2x + 1 = 0 has:Options: Two distinct rootsOne repeated rootNo real root..
Question: If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?Option..
Question: The product of the roots of the equation x^2 + 7x + 10 = 0 is:Options: 10753Correct Answer..
Question: If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?Options: 1234Cor..
