Given Rn = n 6 6 6 0 2 (2 + 10 ) ² - 8 (2 + 10). n n i=1 a = integral, that is provide a, b and f(x) in the expression b= express the limit as ʼn → ∞ as a definite •Sf(x)dx. f(x) = a

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: (x² + 2 , x² – xk – 3 , x 5 7. Find the value of K that makes the function f(x) = Continuous at x =…

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Q: 6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, x), and…

A: Use the formula of Wronskian to determine its values. The functions are already given. Determine…

Q: For the function Sx² - x x² – if x 1 ’ evaluate the left and right limits as x → 1.

A: We can make it easier for you.

Q: Answer 6b. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval…

A: The given ODE is -  y'' + p(t)y' + q(t)y = 0,  0<t<π The given functions which are solutions…

Q: Let f(x) = V4 – x². Then Select one: a. f(x) is increasing on (-2, 0) and decreasing on (0, 2) b.…

A: We know that if derivative of a function f(x) is positive (negative) in given interval then f(x) is…

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

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Q: 2. Compute L4, R₁ and T₁ for the function f(x) = 2 on interval [1, 2]. Verify result from question…

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Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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Q: For what value of k is f(x) continuous at x=3? f(x) = (x-1)(x-3) 9-x² 3k, x=3 " x!= 3 (when x is not…

A: f(x)={(x−1)(x−3)9−x2,x!=3( when x is not equal to 3)3k,x=3

Q: Let f(x) = 36 – 5z – z?. (A) Use interval notation to indicate where f(z) is increasing. Note: Use…

A: Answers are provided below.

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

Q: Calculate Rs for f(x) = 6 - x over ver [3,5]. R8 IE

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Q: Which of the following is the domain of f(x, y) = ln(9-x² - y²)? Ox² + y² ≤9 Ox² + y² ≥9 00< x² + y²…

A: To find the domain of the following function.

Q: The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4…

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Q: Vhich of the following functions is continuous on the interval (- 0, + ∞ )? @ f(x) =Vx²-1 B…

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Q: The domain of the function f(x) = arccos(x – 1) is equal to which of the following %3D intervals?…

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Q: Let f(x)=x²-2x on [-5, 1]. Use the IVT to determine if there is a solution to f(x) = 15 in the…

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Q: Define S = Qn [0, 1] and the function f: SS that satisfies f(0) = 0 and when p and q are 1 coprime:…

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Q: Only one of the following 5 functions is bijective, Find it Select one: O A. f(x) = 2x - 3 from…

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Q: Let f(x) = 0.85x* +x* – 1.26x² – 2.6x – 1. Which of the following is the approximate root x, if x =…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: Find the value of the constant c so the function f is continuous on (-∞, ∞) where f(y) - [cy +9 if y…

A: To find the value of the constant so that the function  is continuous on  where

Q: F:[- 2,2]– R, F(x) = L((- 3(² + 1) dt

A: We have F(x)=∫-2x2(t-3)(t2+1)dt       Apply Liebnitz's rule for differentiation under integration…

Q: S) Let f(x) = {x² –a²x if if x 2 . Find all value(s) of a that make f - ontinuous at 2. Justify your…

A: Given query is to find the values of a for which f(x) is continuous at x = 2

Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm