Show that if f'(x) exists, then we have. lim f(a+h)-f(a-h) = 2f (a) h→0 b

Q: Consider the following. dz Find by using the chain rule. (Enter your answer in terms of t.) dt dz dt…

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Q: You know that: ■ ■ ₁9(t) dt = 15 g(7) = g(9) = 5 Evaluate: +9 юст g'(x) √√25-(g(x))² Upload your…

A: Given:  ∫79gt dt=15g7=-52g9=5 To Find: To evaluate the integral ∫79g'x25-gx2 dx.

Q: 27. f(x, y) = 3x² – 2xy + y² − 8y -

A: The objective of the question is determine to identify any critical points and determine whether…

Q: Find the dot product of the vector pair. u = and v =

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Q: Determine whether the given point (x,y) is on the unit circle. Nin 21 No OYes

A: This is question of calculus  here one point is given  we have to verify that this point is on unit…

Q: The series Σ n=1 convergent. (-1) " n 0.9 Select one: O True O False Give your reasons is absolutely

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Q: British Deficit The projected public spending by the British government for the years 2010-2011 (t =…

A: The projected public spending by teh British Governmnet for the years 2010-2011 (t=0) through…

Q: Determine x = f(t) for dx (t² + 6t). dt = 6x + 6, t> 0; f(1) = 9.

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Q: Evaluate the integral. π [" 10 3x³ cos(x) dx

A: To solve the given problem, we will use following integration formulae ;

Q: Use the integral test to determine whether each of the following series converges or diverges. For…

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Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

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Q: 43. an = 2¹/n

A: By using the appropriate limit laws and theorems to determine the limit of the sequence or to show…

Q: 7. For the function f(x) = xe-, find the intervals on which the function is concave up and concave…

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Q: Given f(x, y) = 9xy + 5xy. Compute: a² f дх2 = a²f = dy²

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find the four second-order partial derivatives. f(x,y) = 3x³y - 5xy + 8y fxx (x,y)= 216x y y (X,Y)=…

A: To find the four second-order partial derivatives. fx, y=3x9y-5xy+8y

Q: Find the differential of the function. z = x ln(y5 + 2) dz = )dx + ( Jay dy

A: Finding a function's derivative is a step in the mathematical process known as differentiation. The…

Q: Write the vector shown on the graph below as a linear combination of standard uni vectors i and j.

A: Graph

Q: lim Δx→0 3 1 x + Δx Δε 1 της X

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Q: дz Use implicit differentiation to find and дх дz дх дz ду || || x2 - y2 + z² - 8z 8 дz ду

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Q: 23. an n √n² +1

A: We take n common from the root and then apply limit to find the vale of limit.

Q: Find the total mass of a 1 meter rod whose linear density 17 function is p(x) kg/m for 0 ≤ x ≤ 1 (x…

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Q: A function fhas a slant asymptote y = mx + b (m‡0) if lim [f(x) - mx + b] = 0 and/or lim [x)-mx + b]…

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Q: Find the component form of vector with initial point (-6, 2) and terminal point (7, -3). O v = (-8,…

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Q: If f(x) da = 16 and ¹ Answer: fr f(x) dx = 3.1, find f(x) dx.

A: We know that the formula int_a^b f(x) dx=-int_b^a f(x) dx

Q: Use the standard Maclaurin series for sin(x) to find the first three non- zero terms in the…

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Q: Find the trigonometric form of the complex number shown below. 10i

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Q: /n³ + 1 n=1 3n³ + 4n² + 2 00 EXAMPLE2 Σ Since an is an algebraic function of n, we compare the given…

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Q: Find the anti-derivative of the func f(x) = = sin (₁+x) - Solve initial Value Problem f(x) = *+^, Y…

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Q: ly the Ratio Test to determine convergence or divergence, or state that the lim n→∞ an+1 an n n² + 1…

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Q: 12-0 dt = + C

A: We know that the integral of x^n dx = x^(n+1)/(n+1)

Q: 7) Refer to the information in Problem 6. Find the object's total distance traveled on the interval…

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Q: Use the limit comparison test to determine whether an = n=12 an lim = lim n→∞ bn n-x n=12 (a) Choose…

A: We have to to Check the convergence of given series.

Q: Construct a limit evaluation problem with an answer of 1.

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Q: Find the magnitude of vector v. -1 1 -1 -2 -3 -4 -5 1 2 V ليا 3 + 4 5 (4,-3) K H

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Q: Find all values of m so that the function  y = xm  is a solution of the given differential equation.…

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Q: 6. For what value(s) of k, does the function f(x) = Ae**, where A is some constant, satisfy the…

A: To find the value (s), for which the function fx=Aekx, where A is some  constant, satisfies the…

Q: Find the component form of vector with initial point (-6, 2) and terminal point (7,-3). O v = (-8,…

A: We need to find the component form of the vector with given initial and terminal points.

Q: 0. Practice similar fxx (x, y) fxy (x, y) = Calculate all four second-order partial derivatives of…

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Q: Evaluate the definite integral. [° ( Z - ²3/) dx J₁ X

A: ∫16x6-9xdx

Q: Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given…

A: Given: Polynomial f(x) has a leading coefficient of 1, has a degree of 7 andhas roots 4,5,3-i and…

Q: 4 -2 -2 -4 h(x). 10 X

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Q: 5. a1 = 2, an+1 = = 2a-3

A: To calculate the first four terms of the sequence, starting with n=1. a1=2, an+1=2an2-3

Q: We now use the substitution u = x6 + 9x and du = (6x5 + 9) dx to convert the entire integral into…

A: We need to convert the integral in terms of u only.

Q: an = 3n 2n + 3

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Q: 6. Consider the following graph of the function f(x) = cos(x). Draw on top of the graph to indicate…

A: Here we have given a function: f(x)=cosx. a) The limit that will compute the exact area represented…

Q: Find the angle between the vectors to the nearest hundredth of a degree. p= and q =

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Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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Q: Find f. II f"(x) = cos(x), f(0) = 6, f'(0) = 4, f'(0)4, "C

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