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Question: Find the value of ∫_0^1 (x^4) dx.Options: 1/51/41/31/2Correct Answer: 1/5Solution: ∫_0^1 x..
Question: Evaluate ∫_0^1 (e^x) dx.Options: e - 1e10Correct Answer: e - 1Solution: ∫_0^1 e^x dx = [e^..
Question: Calculate ∫_0^1 (4x^3 - 3x^2 + 2) dx.Options: 1234Correct Answer: 2Solution: ∫_0^1 (4x^3 -..
Question: Evaluate the integral ∫_1^2 (3x^2 - 2) dx.Options: 1234Correct Answer: 1Solution: ∫_1^2 (3..
Question: Find the value of ∫_0^π sin(x) dx.Options: 0123Correct Answer: 2Solution: ∫_0^π sin(x) dx ..
Question: Evaluate the integral ∫_0^1 (x^2 + 2x) dx.Options: 1234Correct Answer: 2Solution: ∫_0^1 (x..
Question: Which of the following is a necessary condition for a function to be continuous at a point..
Question: For the function f(x) = { x^2, x < 1; 3, x = 1; 2x, x > 1 }, what is the value of f(1)?Opt..
Question: Which of the following functions is not continuous at x = 0?Options: f(x) = x^3f(x) = e^xf..
Question: If f(x) is continuous on [a, b], which of the following must be true?Options: f(a) = f(b)f..
Question: What is the limit of f(x) = 1/x as x approaches 0 from the right?Options: 0Infinity1Does n..
Question: The function f(x) = { 3x + 1, x < 1; 2, x = 1; x^2, x > 1 } is continuous at x = 1 if whic..
Question: Which of the following statements is true about continuous functions?Options: They can be ..
Question: If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x + 1, x > 0 }, what value of k makes f continuous ..
Question: Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } at x = 1.Op..
Question: Which of the following functions is continuous at x = 2?Options: f(x) = 1/xf(x) = x^2 - 4f..
Question: What is the area between the curves y = x^2 and y = 4 from x = -2 to x = 2?Options: 812162..
Question: Find the area under the curve y = x^2 + 2x from x = 0 to x = 3.Options: 9121518Correct Ans..
Question: Find the area under the curve y = x^2 from x = 0 to x = 2.Options: 248/33Correct Answer: 8..
Question: What is the IUPAC name for the compound CH3-CH2-CH2-CH2-OH?Options: ButanolPentanolHexanol..
Question: What is the IUPAC name for CH3-CH(OH)-CH2-COOH?Options: 2-Hydroxybutanoic acid3-Hydroxybut..
Question: What is the integral of cos(x)dx?Options: sin(x) + Ccos(x) + C-sin(x) + C-cos(x) + CCorrec..
Question: Evaluate the definite integral ∫(1 to 2) (3x^2)dx.Options: 5678Correct Answer: 6Solution: ..
Question: Determine the critical points of f(x) = x^4 - 8x^2 + 16.Options: x = 0, ±2x = ±4x = ±1x = ..
Question: What is the second derivative of f(x) = e^x?Options: e^x01xCorrect Answer: e^xSolution: Th..
Question: The roots of the equation x^2 + 2x + 1 = 0 are:Options: -1102Correct Answer: -1Solution: T..
Question: The product of the roots of the equation x^2 - 7x + k = 0 is 10. What is the value of k?Op..
Question: If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?Opti..
Question: What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?Options: 3469Correct Answe..
Question: The quadratic equation x^2 + 4x + 4 = 0 has:Options: Two distinct real rootsOne real rootN..
