1: Find dy if y³-4y² = x³ + 3x². dx 2: Find DPP 7 DERIVATIVE dy dx if sin y² - cos x² = cos y² + sin x². X 3: Find dy if 3x² + 5xy² - 4y³ = 8. dix 4: Find the derivative of 3x² - 4y² +y=9 at (2, 2x-5y² 2 4y³ - x² 5: Find the derivative of = -x at (1, 1).

Q: Use the given transformation to evaluate the integral. J (15x+10y) dA, where R is the parallelogram…

A: INTRODUCTION: The two types of integrals are double and triple integrals, with double integral being…

Q: Question 1 ( (a) ) ) For the function (b) ( transform 3 f(t) use the definition of the Laplace…

A: Given function is (a) f(t)=30≤t<2e2tt≥2and (b) L-13(s+5)(s-2)

Q: DETAILS Use the Comparison Theorem to determine whether the integral is convergent or divergent.…

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Q: Consider the following curve. 1 + x 4 + ex Find y'(x). y'(x) = y = 1 Find an equation of the tangent…

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Q: Differentiate. g'(x) = g(x) = (x + 9√x)ex

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Q: Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value…

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Q: Let g(x) = *F(t) dt, where f is the function whose graph is shown. YA 1 0 3 f 6 9 t O A. Find g(3)…

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Q: Use the translation theorem to find: L{f(t)} A) f(t) = te4¹

A: CONCEPT: According to first translation theorem  Leatf(t)=F(s-a)   so  Lt=1s2

Q: Find the Laplace transformation L {f(t)} if f(t)= (t + 1)² ? s²+2

A: NOTE: Refresh your page if you can't see any equations. . the given function is  take Laplace

Q: Use the graph of f(x) to evaluate the following: 6 + 5 4 3 2 1 -1 f(x) 1 2 3 4 5 X Average rate of…

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Q: 12 C 10 B A 2 F G H D E

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Q: Consider the following system. dx dt dy dt = 6x + 5y K = = -2x + 8y Find the eigenvalues of the…

A: As per guidelines of bartleby we solve only one problem

Q: Evaluate the limit, or type "DNE" if the limit Does Not Exist: x²-xy √x-√Y lim (x,y) → (3,3)

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Q: sin³ x + cos²x sinx = 2

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Q: Find the volume of the solid bounded below by the circular paraboloid 2 = x² + y2 and above by the…

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Q: Find 5 [(7x³ + 3x³) dz

A: use the algebraic property of integrals.

Q: Differentiate. y' = у 4x 3 - tan(x)

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Q: Find the four second-order partial derivatives. 5 f(x,y) = 2x y-5xy +9y fxx(x,y) = fxy(x,y) = fyx…

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Q: ind the equation of the plane that contains (1, -2, 1), (1, 0, 2) and (0, -2, 2)

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Q: Consider the following function: Step 4 of 4: Enter the x-values of any local Answer Separate…

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Q: Which of the following represents a geometric sequence with a common ratio r = 5?  1 2, 10, 15, 75,…

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Q: Let C be the curve f(x) = the length of C, as follows: (1) Calculate f'(x). In(x) 2 - 4 between 1…

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Q: Differentiate. y' = y = 3 sec(x) - csc(x)

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Q: 2 sin 0, 3. Find a "cartesian" equation for the circle which is given by the polar equation r = and…

A: The polar equation is  r=2 sin θ

Q: How many units is the arc length of the curve y = point where x = 3? ³/2 from the point where x = 0…

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Q: 8) The Bernoulli's equation += dz NIH 2 218 I can be reduced to which linear differential equation?…

A: Ode

Q: The function w(z) represents a package's corresponding weight in grams when the package's weight is…

A: Given query is to find the meaning of the inverse function.

Q: Explain the relationship between a function and the derivative by providing an example.

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Q: 3. Write 2.734234 = 2.734234234... as an improper fraction.

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Q: The volume of a balloon is inflated from 0 to 8 m³ in 5 minutes. What is the average rate of change…

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Q: The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 14…

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Q: Find the linear approximation to the equation f(x, y) approximate f(6.28, 4.16). f(6.28, 4.16) xy at…

A: Given  fx,y=5xy6 The objective is to find the linear approximation to the equation.

Q: Consider the following functions. f(x) Find (f + g)(x). = g(x) = Find the domain of (f + g)(x).…

A: Domain of a function y=f(x) is the set of values of x for which f(x) is defined.

Q: Suppose that lim = f'(0). Select the correct answer for the limit indicated below. x→0 X f(x) Select…

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Q: • L₁²*²1*²** LI Q16: 2z√x² + y² dz dy dx (Hint: use the cylindrical coordinate)

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Q: rting to polar coordinates. dy

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Q: What is the inverse of the function f(x) = (x-6)2 where x ≥ 6, if it exists?

A: Given: f(x)=x-62

Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: If g(x) = f* √u² + 2 du, what is d²g / dx²? 0

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Q: Find the derivative of the function g(x) = (5x² + 5x − 2) ex - g'(x) =

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Q: 1) Determine the solution of the differential equation dy x +y = r² + r da

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Q: 16. If h(x) = f(2t +Vt) dt, find h'(-2).

A: If hx=∫0x32t+t3 dt, then to find h'-2.

Q: (6417 #3 p. 357) Find the average value of f(x) = 6r-r² f(x= on the interval 2<z≤8

A: Given function is f(x)=6x-x2 and the interval is 2≤x≤8.

Q: (4) y = Tan' (*); d =? A) 4 4+x² B) 15) ys A) 2 SecX 11 2√4-X² Sec (X); dy = ? +Y 2 secx. ranx D)…

A: 16) The given equation is; Sinx - Cosy - 2= 0

Q: Consider the following functions. f(x) = x², g(x)=√x-7 Find (fog)(x).

A: Given,            fx=x2 , gx=x-7

Q: Find the points at which the following polar curve has a vertical or a horizontal tangent line. r=8…

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Q: Solve the following recurrence relations: (a) an = 3an-1-2, ao = 0 (b) an 2an-1+(-1)", = ao = 2 (c)…

A: Since, you have posted question with subparts. As per guidelines, we are supposed to answer only…

Q: Consider the following function: f(x) = −x4 + 8x2 + 2   Enter the x-values of any local minima,…

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Q: Given that ƒ(x) = x² − 8x and g(x) = x + 5, find: a) (fog)( − 1)= b) (gof)( − 1)=

A: Given query is to find indicated composite function.

Q: ) If we would like to solve the following differential equation by variation of parameters 3x then…

A: We check whether the statement is correct or not .