Evaluate the integral. 1 (4 + r)3 dr

Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: 7. Find the absolute maximum and absolt f(z) = 2x – 31²/3 on the interval -1,2). %3D

A: We have to find out maximum and minimum

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: Evaluate (x - 4y + z) ds. S: z = 5y, 0 s x s 4, 0 sysx

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Q: А. f(x) 3D Vx + 1; а %— 6 if x > 1 if x < 1 a = 2 С. f(*) — 13х + 1l; а %—-+ a = (3х — 2 В. f (*) —…

A: Only Function given in (C) is continuous at that point but not differentiable at that point. For…

Q: 3 sin z If f(2) = then 2 + cos z f'(2) =| f'(5) -

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Q: a. f(x) = V3x3 – 2 %3D b. y = (Vx + 1)(x² – x) 2x5-3 c. f(x) cos x d. y = sin(4x²)

A: All the questions are solved below.

Q: Find the area of the region enclosed by y = 5x and x = 6.5 - y. 2- 3 4 5 6 Use horizontal strips to…

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Q: Evaluate the integral sin3 x + cos? x + 1 dx J sin² x (cos² x + 1)

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Q: An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is…

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Q: For the function f(x) given below, evaluate lim f(r) and lim f(x). -2+ 3e f(a) - 6e +4 If the…

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Q: Find the equation, in slope-intercept form, of the tangent line to the curve defined by the given…

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Q: Evaluate the integral (2х — 8)dx х2 — 6х + 18

A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

Q: Sketch the region enclosed by x + y = 42 and x + y = 0. a) Favoring convenience, should you…

A: Given; x+y^2=42 , x+y=0

Q: -ide each of the fol x-4x²+2x-3 x+2

A: Solve the following

Q: A spring has a natural length of 30 cm. If a 27 N force is required to keep it stretched to a length…

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Q: The functiof(x) and it’s first and second derivative are given: A) Domain of f(x) B)y intercept is…

A: Solution: f(x)=x-2x3 a) Domain :  take the denominator and compare it to zero x3 =0 =&gt; x=0

Q: Solve: (2y cos x + sin* x) da 4 = sin x dy O y csc x + cos ¤ = O y csc x – cos a = C O y csc? x +…

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Q: Find the flux of F across S, F.N dS where N is the upward unit normal vector to S. F(x, y, z) = xi +…

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Q: 5. Determine the vertical and horizontal components of each force. a. 810 N at an inclination of 75°…

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Q: (a) Evaluate the double integral.

A: answer is in next step

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

A: This question can be solved using the concept of compound interest.

Q: Solve the differential equation. Show your complete and clean solutions. 2 (x-y) dx + dy = 0

A: The given DE is: 2(x-y)dx+dy=0⇒dydx=-2(x-y)⇒dydx=-2x+2y⇒dydx-2y=-2x...(1)

Q: E) Find the line's equation which passes through the points (2 , 5), (-3, 1)?

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Q: An ellipse has centre (0,0) and vertices on the y-axis. The minor axis has length 10 and the major…

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Q: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

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Q: y = y (4, 13) 12

A: We will find the exponential function.

Q: Find the marginal cost, marginal revenue, and marginal profit functions. C(x)=4x; R(x)=6x-0.001x^2

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Q: What are the slopes of the asymptotes for the hyperbola whose equation is 4x2-9y? = 36? %3D

A: Here, the given equation of the hyperbola is: 4x2-9y2=36 In standard from it can be written as:…

Q: 5. (r' -12r +43r? - 41r +5)÷(r –5)

A: Given query is to perform long division.

Q: Use the quotient rule to find the derivative of 3 sin(2) – 10 925 – 9 You do not need to expand out…

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Q: Use the acidity model pH = -log[H*], where acidity (pH) is a measure of the hydrogen ion…

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Q: COS X To check for the result, prove that CSC X+ 1- cos x xp Evaluate the lee cida nE the onuntion

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Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 1)²

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Q: 12x° + 45x + 100x + 8 and classify them using a Find the critical numbers of the function f(x) :…

A: Solution: f(x)= -12x5 +45x4 +100x3 +8

Q: (a) Evaluate the double integral. бу 4x5 + 1 dA, D = {(x, y) |0sys 1, vỹ s xs 1} (b) Evaluate the…

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Q: 7) y=-4x 8) y=7 9) y=x

A: We have to differentiate

Q: 6. Since 3 is a constant, use the following property of summation to find the sum 3i- | = 1 E ka; =…

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Q: Determine the indefinite integral 6.xV-5]7 dx by substitution. (It is recommended that you check…

A: We have to solve  ∫6·x3·x43-57 dx.

Q: Dose the h partial sum of a series a, is as follows. n = 1 -ח n+ 5 Find and n = 1 Step 1 We are…

A: Solve the following

Q: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: Example 9 Video Example4) Evaluate the integral. In(x) dx Solution dx occurs in the integral. When x…

A: Given query is to find the value of the integral.

Q: D is some triangular domain in the xy-plane with area equal to 9. S i the triangular area that is…

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Q: dy = 2xV1 – y², 17. -1< y < dx

A: We have to find out solution

Q: (c) Let f(x) for x * -K %3D (x+ K) (i) Find f(x). (i) Use the result in (i) to find the function g…

A: To find out the f-1(x).

Q: What is the equation of the tangent line to the curve defined by the given function at the point…

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Q: dy Given the equation below, find dx 39x + 10ay + y° – 28 = -

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Q: The first along term of a sequence with a (ecursion formila e the lemaing terms for- B given beloN.…

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Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x    Given