3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: Think back to early in the semester when the weather was cold and often snowy. Imagine that in a…

A: Concept: Here we have the height of the mound is 24 inches (h) And the base of the mound is 36…

Q: Which of the following describes the graph of h(x) = −3(x − 1)²(x + 1)²(x + 2)? O-12 O -10 -0 -4 -12…

A: see below the answer and explanation

Q: Rewrite the expression In 3 + 5 ln x + 6 ln(x² + 4) as a single logarithm In A. Then the function A…

A: We know the property of logarithm that  ln(a)+ln(b)= ln(ab)  ...(1)  And,  pln(x)= lnxp .....(2)…

Q: 900mL of lactated ringers is infusing at a rate of 42gtt/min.  The drop factor is 60gtt/mL.  How…

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Q: If f(x) = 1/√x, use the definition of the derivative to find f'.   You must show ALL of your work…

A: The given problem is solved below in detail.

Q: The following function is positive and negative on the given interval. f(x) = 8 - 2x²; [0,4] a.…

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Q: dr. (4+x²)²

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Q: 1. y = Arccos 1-x

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y = r sin(8), and note that (x,…

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Q: X y = x + Ae^ + Be - 2x

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Q: Solve differential equation dx -(2ln5y+x-¹) 2xy-1

A: Solution is given below:

Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j - k, find: (iii)A. (B+C)and (A + B).C (iv)…

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Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: J 24 tan3 xdx

A: topic- indefinite integral

Q: what about part (b) please.

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Q: 7dx x(lnx + 1) S:

A: To solve the given integral problem by substitution.

Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…

A: To find domain and range of the given function.

Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Evaluate: x5 exdx when a and b are limits of integration such that a is the numerator and bis the…

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Q: Use logarithmic differentiation to find the derivative of the function f(x) = (sin 7x)/x c) Coal is…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

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Q: Approximate the area of the region bounded by the graph of f(t) = cos (t/2/2) and the t-axis on…

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Q: 31-4 A piecewise function f(x) is defined by f(x)=x²+3x+4 x² -7x+12 Part A: Graph the piecewise…

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Q: -2y²z3,-4xyz3, -6xy²z²)

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Q: 5. 2π π [[(sinx + cosy)dxdy πο

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Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: QUESTION 1 Let I = fxe³x. To solve I, we need to apply O Integration by substitution O Integration…

A: The answer is given below.

Q: [ 81e-9 sin 9xdx

A: Please see the below picture for detailed solution.

Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

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Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: Describe the level curves of the function. z=x+y, c= -2, 0, 2, 3 O The level curves are parabolas.…

A: We need to choose correct option.

Q: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)

Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: Find f(145) (x) for f(x) = 83x¹0⁹. Simplify your answer completely. f (145) (x) =

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Q: The volume of the solid obtained by rotating the region enclosed by y = x = 1, x = 7, y = 0

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Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

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

Q: Evaluate: AT -dx B. 이집 는 d 를

A: Evaluate the integral ∫0πxsinx1+cos2xdx

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

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Q: What is the radius of the circle defined by x + y - 6x + 4y - 1 = 0

A: Given : x2+y2-6x+4y-1=0 To find radius of circle

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A: topic- indefinite integral 2sinθcos(θ)=sin(2θ)sin2(θ)=1-cos(2θ)2

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→2…

A: The limit is evaluated below.

Q: sin 8 cose √cos²0-9 c. f S do

A: Since, we have been asked to solve Part-C in which we have to evaluate the integral given…