In which limits below can we use L'Hospital's Rule? lim 818 Olim 848 Olim 48 Olim €8 et X In x e X H 3x² + 4x + 6 x² + 2x - 9

Q: y = 3x-2x²+x-5; y""

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Q: If f(x) = 7x² f'(2) = f''(x) = f''(2) = 8e, find:

A: The given function is fx=7x2-8ex

Q: 9) Let R be the region bounded by the graphs of f(x) = cos(x) and g(x) = sin(x) where ≤x≤. If T is…

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Q: Evaluate r2 ff dyda.

A: Given itegration ∫-12∫x2-2x   dy dx

Q: polar curves. 63. The complete circle r = a sin 0, where a > 0

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Q: simplify the function before differentiating f(x)= 1/square root e exponent 9x

A: Topic = Differentiate

Q: Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

A: This question is related to slope of line, we will solve it using given information.

Q: Evaluate the following integral using integration by parts. 4x sin 4x sin x cos x dx Let u=4x sin x.…

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Q: I need the integration solution in the easiest way, a step-by-step solution and a clear line, please…

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Q: Find the indicated midpoint rule approximation to the followin S 4 sin (x) dx using n = 6…

A: The Midpoint Rule: ∫abfxdx=∆xfx0+x12+fx1+x22+fx2+x32+...+fxn-2+xn-12+fxn-1+xn2 Where, ∆x=step…

Q: Phyllis invested $9,500, a portion earning a simple interest rate of 8% per year and the rest…

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Q: (8) A SUPPOSE VECTOR FIELD FY₁Z) =<X₁Y+Z₁ HAS PARAMETERIZATION z(t)=7+4 AND A x) = ²x WHERE CURUE C…

A: A detailed solution is given in steps 2 and 3.

Q: Use linear approximation, i.e. the tangent line, to approximate √49.4 as follows: Let f(x)=√x. Find…

A: For function, f  the linear approximation at a is given by L(x)=f(a)+f'(a)(x-a)   ...............(1)…

Q: Find the third degree Taylor polynomial centered at a = O T3(x)=3+3x+3x²+3x³ O T3(x)=3-3(x-1) +…

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Q: Find the area enclosed by the polar r = 2 (1+sine) Curve

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Q: 4. consider F(x, y) = (y² − 2xy) i + (2xy − x²) j. (a) Show that F is a conservative vector field in…

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Q: Use the product rule to find the derivative of (4x⁹7x¹)(5e* - 4) Use e^x for e. You do not need to…

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Q: Show the complete solution. Kindly, include the necessary table of values. 6. If a thermometer is…

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Q: 1 8. The equation of the image when the line y = x + 1 is translated through (3,-1) is? 1 a. y = x +…

A: Please see the below picture for detailed solution.

Q: Find the average value of the function over the given interval. F(x) = = 2₁ [4, 6]

A: We have to find the average value

Q: Evaluate the integral and choose the correct answer. Sin In x dx

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Q: (b) Determine whether the series Σ n=1 5n cos(3n) 2en converges or diverges.

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Q: n=1 3+2n-1 4n

A: Topic- sum of a geometric series S∞=a1-ra=first termr=common ratio

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: We will find the required.

Q: 2(3+3+9-8)-6

A: Given data:- 2(3+3+9-8)-6

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: (x + 2y) dx + (2x + y) dy = 0. ANS. x² + 4xy + y² = c.

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Q: Find the exact value of the indicated trigonometric functio 2 =, , tan 8 <0 Find sin 8. cos 0 =

A: answer is in next step. please give a like !

Q: Bottom of the page is cut off i cannot see the solution.

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

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Q: Evaluate O 10 • 4 5 9 2z plny Մ » 0 -T ye dædy dz.

A: To evaluate the integral.

Q: Find the power series representation of the function f(x) = = x 2x² +1'

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Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 x=y³ 0.5 x = y² 1 (1,1) X 1.5 C The area is

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Q: a. b. n=1 8 n någn-1 (-5)n 1 nVn? +1

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Q: potential

A: Please refer to the image below

Q: Determine whether the vector field F(x, y) = conservative. yi + xj 1 + xy is

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Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: Consider the following differential equation: y" + y = sinx - 2e and the following boundary…

A: The given differential equation is y''+y=sin x-2ex

Q: at a price of $55

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Q: Use substitution method and find the indefinite integral Adx

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Q: Question 3 A dilution tank initially contained 100L of fresh water. Then water which contained…

A: As per our guidelines answer first three subpart of a multipart question. So please resubmit the…

Q: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

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Q: A silver dollar is dropped from the top of a building that is 1322 feet tall. Use the position…

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Q: O O 2x4 1,34 dx +1 NIS In[x5 + 1] + € C In[x5 + 1] + C 5 In[x 5 + 1] + C In[x5 + 1] + C

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Q: A manufacturer wants to design a rectangular box with a square base and an open top. (In other…

A: Let  side of square = x  height of box = y    surface area = area of base + 4 * area of side face…

Q: If f(x, y) = ecosy, then find Ꭷ f Ꭷ2 f + Ox2 " dy2

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Q: 6)    State whether the series converges absolutely, conditionally, or not at all. ∞ n = 1 (−1)n +…

A: The given series is ∑n=1∞(-1)n+1n+9

Q: y= e2x+1 e-1

A: