Find the vertex, focus, and directrix of the parabola, and sketch its graph. y² = -16x

Q: 1. Given y = ax³ + bx² + cx. Find a, b, and c so that the graph of y will have a point of inflection…

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Q: Find the equation for any horizontal asymptotes for the function below 3-7x+x² 2+9x+6x² f(x)=- FOTO…

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Q: Evaluate SS √1 + x² + y² dS where S' is the helicoid: r(u, v) = u cos(v)i + u sin(v)j + vk, with 0…

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Q: f(x, y) = e 10x-z²+8y-y² Find and classify all critical points of the function. If there are more…

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Q: Suppose that the demand of a certain item is Q 100e-0.02p. Remember, elasticity is given by the…

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Q: 31 If f(x, y) = e³¹ sin 9y, then fry is given by:

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Q: Evaluate each of the following definite integrals by using its geometric interpretation. 13 (a) f.¹³…

A: Let's evaluate the given definite integral by using its geometric interpretation.

Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 1 and roots of multiplicity 1…

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Q: Problem 1. convergent or divergent. ∞ 1 n=1 n Use the Integral Test to determine whether the…

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Q: 9. The area of the region S that lies under the graph of the continuous function is the limit of the…

A: Please see the below picture for detailed solution.

Q: find the area that is bounded by the curve ? = √(10sin(theta)) and lies in the sector 0 ≤ theta ≤ pi

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Q: Where does the relative maximum value of f occur when f'(x) = x³ - x? (a). -1 (b). 0 (c). 1 (d). 2

A: concept first find x when f'( x ) = 0 if f''( x ) < 0 then maxima will occurs if f''( x ) > 0…

Q: Find differential of the function y = dy = dy When x = 3 and dx differential. dx. = = (x²+4)³. 0.05,…

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Q: Prove that, a.) lim X10 b.) lim X O 3x + 1 X+1 sin x X 1 1

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Q: Graph and label (w/ letter) the following points given in polar coordinates. A(7.) A 7,- B(5,-2) D…

A: we need to graph the polar coordinates and have to label them.

Q: Find the area of the graph enclosed by y=7x and y=4x2

A: Given:     Curves y=7x                 y=4x2 The area between the curves is the area between a curve…

Q: Find the time required for an investment of 5000 dollars to grow to 8100 dollars at an interest rate…

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Q: Determine if the vertex of the graph of the equation is a maximum or minumim point. y=x²+4 vertex is…

A: Given query is to find verteyis maximum or minimum.

Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (b)…

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Q: Find the general solution of the HLDE (D2 + 2D + 1)(D2 + 4)? = 0

A: The given equation is; (D2 + 2D + 1)(D2 + 4)y = 0

Q: . Зп 2п f (x) dx

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Q: Assume the bucket is leaking.It starts with 5 liters of water (5 kg) and leaks at a constant rate.It…

A: We need to find work done.

Q: g(x) = (x − 2)(3x + 1)(x + 4); only power rule

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Q: Let f(x) be a continuous and increasing func [F(t)di 0 0,00) and let F(x)= X '(x) is increasing on…

A: Topic:- application of derivatives

Q: Consider the following initial value problem, defined for t > 0: dy dt a. Find the Laplace transform…

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Q: 1. Consider the sequence an = cos² 3πn² n²-5 a. Does the sequence converge, or not? If it is…

A: To determine whether the given sequence converges or not

Q: The angle of elevation to the top of a Building in New York is found to be 6 degrees from the ground…

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Q: Solve the following differential equation, subject to the given initial condition. dy x +(1+3x)y =…

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Q: A spherical balloon is being inflated with helium at a rate of 201 cm³/min. How fast is the…

A: topic - application of differentiation

Q: Find the point on the plane x - 2y + 3z = 9 that is closest to the point (0, 2, 1). 5 3 23 8'4'8 )…

A: The equation of the plane  x-2y+3z=9

Q: Show that the vector field F = is not conservative by showing it is not path independent.

A: We have to show that given vector field is not conservative. Topic:- Vector Calculus.

Q: 2. a) d) 2 9 T 4 b) e) 5 T 4 13 п 4 c) 2TT f) 23 TT 4

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Q: Which one of these expressions is not equivalent to the other two? Select the odd one out. A (В B a.…

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Q: The vector equation r (u, v) = = u cos vi + u sin vj + vk, 0 ≤ v ≤ 8π, 0 ≤ u ≤ 1, describes a…

A: Given that , ru,v=ucosvi+usinvj+vk and 0≤v≤8π , 0≤u≤1 find the surface area.

Q: 4. FIND THE 2ND DERIVATIVE f(x)= (3x²-2)bog (3x²-2); x Solution: x=1

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Q: t on the interval [-3, 0]. 1² +1+1 (Express numbers in exact form. Use symbolic notation and…

A: Given, R(t)=tt2+t+1

Q: Graph the function over a two-period interval. y=-2-- tan 2 x + 1 2 2(x+. 3r 2

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Q: Suppose F'(x) = 5x² + 6 and F (0) = 1. Find the value of F (b) for b = 0, 0.1, 0.4, 0.8, and 2.0.…

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Q: 103.3 5 [ ₁ (+² -5 (x² + 2) dx X

A: ∫xndx=xn+1n+1+clet I=∫-55(x2+2)dx

Q: Find a critical number of f when f'(x) = 2x³ + x² – 3x. (a.) x = NIW 2 (b.) x = 1 (c.) x = -1 (d.) x…

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Q: Evaluate the surface integral ff 3x² ds, where S is part of the surface of a paraboloid with…

A: Given:- ∫∫S3x2ds S is part of surface of paraboloid with parameterization ru,v=vcosu,vsinu,v2 Where…

Q: Find the area of a triangle whose sides measure 50 inches, 22 inches, and 36 inches.

A: To find the area of a triangle whose sides measure 50 inches, 22 inches, and 36 inches.

Q: a) [x²e³dx

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Q: Solve the linear system of equations by elimination. X + y + z = 7 + y - Z -1 -2x + 3y - = = 15 ४ -…

A: Given, x+y+z=7x+y-z=-1-2x+3y-z=15

Q: Determine the projection of the surface - y² = z on the xy- plane? (Hint: z = 0) O One Line O…

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Q: 2. Find the sum of the series. ∞ 71=0) 312-4¹ 5n|1

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Q: suppose gradient f(a,b) =4i + 3j. find a unit vector u such that a) Du f(a,b)=0 b) Du f(a,b) is a…

A: Please see the below picture for detailed solution.

Q: 6.(x-2) dx

A: Definite Integration is the area under curve.

Q: 42. Given that "sin'x dx-, what is sin¹0 do?

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Q: Solve the FIRST ORDER LINEAR D.E. sin e Linear in r dr de = -1- 2rcos 0

A: To solve the given linear differential equation