Calculate the derivative of y with respect to x. Express derivative in terms of sin (y³) (Express numbers in exact form. Use symbolic notation and fractions where n e4xy M dy dx Incorrect 11 - 5u(exy) (4y³ cos (14) – 5x(e5xy))

Q: Let C be the curve y = 12 11 10 9 8 7 16 16 5 A m Cy 1.5 x³ 1 + for 0.6 3.7. 3x 4 2,5 3 Find the arc…

A: We are given a curve C : y= x3/4 + 1/(3x)  for 0.6≤x≤3.7. We have to find arc length of C.…

Q: S cos 2x dx COSX

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Q: f(t) = sin(wt) u(t) Do the laplace transformation of the math in details.

A: we have F(t) =sin(ωt) u(t)

Q: Consider the equation below. (If an answer does not exist, f(x)=x²-x-In(x) (a) Find the interval(s)…

A: We have given a function and finding point for local minimum value

Q: Find a plane containing the point (-1,-7,-8) and the line of intersection of the plan 6x + 4y + 4z =…

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Q: z=(4xy)/[(x^2)+(y^2)] (a) (partialz)/(partialx)

A: We have to find the partial derivative.

Q: The data given in the Table below is produced from a Linear Difference Equation model of the form: Y…

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Q: Evaluate the following integral or state that it diverges. ∞0 J4e-4 -4x dx Select the correct choice…

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Q: Find the derivative using logarithmic differentiation. x(x+4) (5x + 1)(3x +7) y =

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Q: Surface integral is used to find Density O O Area Surface Volume O

A: We can find the answer as below.

Q: Find the equation of the curve at every point of which the tangent line has a slope of (1+y^2)/2xy…

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Q: Write an equation for a sphere centered at the point (4,7,2) with radius 5.

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Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

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Q: Two functions fand g are defined in the figure below. (a) ∞ Domain of f (b) Range of f 7 9 Domain of…

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Q: Let R be the region bounded by y = x², x = 1, and y = 0. Use the shell method to find the volume of…

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Q: Consider the graph of r(t) given below. -4- 2 |_y=r(t) 0 2 C) Find r' (2). [Select] 4 D) Find r'…

A: Given that graph of y=rtA.gt=sin3πrtg't=cos3πrt×3πr'tg'1=cos3πr1×3πr'1r'1=slope at…

Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and 6=. (a) Find the unit vector u…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and 6=. (a) Find the unit vector u…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: The Taylor series for f(x) = eª at a = -4 is Σ ²n(x + 4)" n n=0 Find the first few coefficients. со…

A: The solution is given below

Q: 100 100 suppose that Σ a; = -17 and Σ b; = 13. compute the sum. i=1 i=1 100 Σ ( – 30a; – 76;) i=1

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Q: 5. (8 pts) An isosceles right triangle is as shown in the figure. The leg is increasing at a rate of…

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Q: ey+5 | ey-5 ولا

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Q: A 2 In Ix-11+C B 2 In 1x-11-2+C S dx 2x (x-1)² C¹In Ix-11+C с D 2 In 1x-11+2+C

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Q: Find the curvature K of the curve. r(t) = et cos(t)i + et sin(t)j + et k

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Q: A boat is heading towards a lighthouse who's beacon light is 148 feet above the water. The boat's…

A: Topic = Trigonometry

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. csc(x) = 4, tan(x) < 0 sin (2x) =…

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Q: B) Find the interval of convergence for the series n=0 xn √n² +3

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Q: determine whether the given series converge or diverge. 20. (-0.99) ¹+1 n=5

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Q: 3 Approximate (4+x²) dx using five equal subintervals. -3 An approximation for the integral using…

A: To approximate ∫-334+x2 dx by using five equal subintervals.

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: Using triple integrals, calculate the volume of the set in 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤z<5-x²-y² Ps:…

A: Find Volume of the set in 0&lt;=x&lt;=1, 0&lt;=y&lt;=1,&lt;=0z&lt;=5-x2-y2 .

Q: f(x) = (x + 6)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated…

A: Given that fx=x+623a.find f'x=0 and solve x is a critical numbers.fx=x+623f'x=23x+6-13f'x=23x+613so,…

Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is then pumped…

Q: Evaluate the definite integral. 2 cot-¹(x) 1 + x² 1 - 1 dx

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Q: Emptying a tank A vertical right-circular cylindrical tank mea sures 30 ft high and 20 ft in…

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Q: Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x)…

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Q: Which of the following is a unit vector parallel to the vector ? Select one: 2 0 8 1 4 <- 81¹ 81¹…

A: Let's solve.

Q: 16. A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x)…

A: We need to find P(x).

Q: Suppose that csc a = -(√5)/2  and 180° < a < 270°. Find the exact values of sin a/2 and tan a/2…

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Q: Let f(x) = { 3x² +2, if x < 2 2x - 3, if x ≥ 2 be a piecewise function. Evaluate [₁ f(x)dx= [

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Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: Find the constant of variation when one exists and write it in simplest form. Direct variation…

A: We have to find out solutions

Q: Differentiate the function 3 H(x) = (xx+x¹) ³ H'(x) =

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Q: The equation x² + y² +10y + z² = 6z - 18 represents Select one: O a sphere with center (0, 5, -3)…

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Q: Find the position of a body moving on a coordinate line at time t for an acceleration a= dt² initial…

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Q: Compute the given improper integral. Enter the exact value of the answer. 1 /x² 400 29 So - dx =

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Q: The one-to-one functions and h are defined as follows g={(-4, 5), (0, 6), (4, 2), (7, 4)} -…

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Q: Evaluate the expression under the given conditions. sin(20); sin(0) ==, in Quadrant II 0

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Q: Use the table of Laplace transforms to find the Laplace transforms of the following cos² 2t sint cos…

A: Topic:- Laplace transform