2. Find y' if y = 7* (log4 x)⁹.

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A:

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A: Given 9y''+9y'-4y=0To find general solution of D.E.

Q: Q4A/ If y=x sinx+√1-x², then dy/dx is: 1.√1-x² sin-¹ x 2. sin(x) O 1 O 2 x cos(x) sin(x) sin(x)2

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Q: Determine whether the differential equation (7x+8) + (7y - 7)y' = 0 is exact. If it is exact, find…

A: To determine that the differential equation is exact or not.

Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

A: Given problem:-

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A: I am attaching image so that you understand each and every step.

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Q: consider the function f, such that f and f are continuous for t > 0 defined by: 0<t<7 f(t)= -68t…

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

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Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: If y = ecos(x) then y" + sin(x) y' cos(x)= ***

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: -32 1 ย X

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Q: 7- cos y dx + (x siny - cos²y)dy = 0

A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: 5. Determine the area below f(x) = 10 - 2x² and above the line y = 3. 6. Determine the area bounded…

A: Given problem:- Determine the area below f(x) = 10 - 2x2 and above the line y = 3

Q: (d) f(x)=√√x-8 (e) h(x)=√x+2

A:

Q: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: ind the equation the tangent line and normal line to the graph of f(x) = x³ at x = 2.

A: Given f(x)=x3 substitute x=2 in f(x)⇒f(2)=23=8 The tangent line passes through the point (2,8)…

Q: In the Figure 1, if Q= 40 N, P = 50 N, and B = 145°, then R is equal to (in N): Figure 1: C R A Q B…

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Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: xe5x dx (5x-1) i 51 e³z B.5 (5x-1)+c C. 5x+ E

A: We will solve the problem.

Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

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Q: Prakash is on a hiking trip. On the first section of the hike, he walks 5 km from the Hawk Campsite…

A: Given that Prakash walks 5 km from Hawk campsite(A) to the Condor Campsite(B).  Then, he turns and…

Q: d dx [47 tot 1 3x17 5 13 + 10 L 25 +100

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Q3. Use the integral test to determine whether the series, n=1 divergent. 1 (n+1)√n+1 is convergent…

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Q: Find the average rate of change of f(x) = 8x² − 4 on the interval [5, a]. Your answer will be an…

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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

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Q: 2. Show that the function. 5x²³²Bin 12 F(x)= โ x2 0 (x=0) is not of bounded variation on [1,1].…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Solve the triangle ABC if b = 127, c = 163, ZB = 40°. a = ZA = degrees; ZC = degrees; Assume ZA is…

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Q: Use the table of integrals to evaluate the integral. 2 [²³15x³√4x² 15x³ 4x²x4 dx

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Q: dy dx Using logarithmic differentiation, find NOTE: Express your answer in terms of x only. dy dx =…

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Q: Question 11 Evaluate the limit lim (ln(3x² + 2) - In(x² + 1)) O ln 3 O In 3 01 00 O ∞

A: To evaluate the following limit.limx→∞ln3x2+2-lnx2+1

Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

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Q: the function. 4) ((x) = fx+3, for x>0 [x², for x ≤0

A: Given above function is x+3, for x&gt;0x2, x≤0

Q: 7. Determine the area bounded by y = x² - 6x + 10, x = 1, x = 5 and the x-axis.

A: Above question is solved.

Q: Circular Ring Method 3. R: y = x, y = 2x axis of revolution: x − axis

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Q: D Question 15 Find the value of b such that the function f(x) is continuous everywhere. x² + a if x…

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Q: Use the graph of h(x) shown below to evaluate limh(x), if possible. If the limit does not exist,…

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Q: Find the volume generated by revolving the given plane area about the given line using disc method.…

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Q: A) Find all value(s) of a such that lim f(x) does not exist [Select] B) Find all value(s) of b such…

A: Question 8 A) limx→1-f(x)=6≠limx→1+f(x)=4 limx→2-f(x)=-∞≠limx→2+f(x)=∞ answer: a=1 and a=2 only