15 y = f(x) is the parabola shown. a Find f(3) and f'(3). b Hence find f(x) in the form f(x) = ax² + bx + c. 14 y=f(x)

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Q: Answer TRUE or FALSE. The general solution of a 2nd order non-homogenous linear ODE of the form…

A: The answer is in step 2.

Q: 9 point of inflection of f(x) = (45x) if there exists. 5

A: Find the point of inflection of f(x)= 45x95, if there exists.

Q: Outcome: Find the absolute maximum or minimum value of a quantity subject to given constraints. MATH…

A: NOTE: Refresh your page if you can't see any equations. . as per your request, we will solve…

Q: Write the number 2.317 = 2.3171717... as a ratio of integers.

A: Given number :- 2.317=2.3171717.....

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Q: 7- Minimize the material needed to design a rectangular cubic box of volume 900 cm³. Find the…

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Q: Motion Problems with Trig (Level 2) Nov 14, 10:09:16 PM A particle moves along the x-axis with…

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A: Given: I=∫-22∫04-x2∫3x2+3y216-x2-y2y·dz·dy·dx Now solving the given triple integral we get:…

Q: Find all antiderivatives of the given functions: 2x4 - 3x² +5 x² Hint: Simplify f'(x) first. (a)…

A: To find the antiderivative of the given function.

Q: The limit of the sequence {In(7n) - In(9n+8)}_₁ is

A: To find the limit of the given sequence

Q: Diagonalize the matrix A || -1 −1 1 4 16 by writing it as A = PDP-¹

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Q: the graph alongside to find

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Q: 4 So 1 √x (1+√√x) Α) B D In 3 In 5 2 ln 3 da is divergent

A: To find the integration.

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Q: 7. Verify algebraically cos(0) sec(0) + sin(0) csc (0) = 1.

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Q: the x = 4 axis using the method of disks. 0 (0.25, 4) y=1/x V = T y = 4 OV = 2π 0.25 (4) dy OV=T 25…

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values y₁ Y2 Y3 and Y4 of the…

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Q: Find the Taylor series Σ n=0 f(n) (9) = R = for f centered at 9 if (-1)^n! 3^(n + 2) What is the…

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Q: 3. a) Find the point on the line y = 2x+3 that is closest to the origin. b) Find the points on the…

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Q: a) For each of the following improper integrals, evaluate the integral or show that the integral…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: . Find ھے { n=1 Fract Sum 224 124

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Q: Use Green's theorem to compute the area of one petal of the 16-leafed rose defined by r = 14…

A: Let's find area of one petal.

Q: Find all values of X that will satisfy the equation within the interval 0 < x < 2π: cos X cot X…

A: Given: So,…

Q: 3 1/3 divided 6

A: Given query is to find value of the Indicated expression

Q: 9- Find 5√10 – 3x² dx

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Q: Evaluate the geometric series or state that it diverges. 2.3k 5k Σ k=3

A: Given, ∑k=3∞2·3k5k

Q: Find the absolute extrema of f(x) = 4x6/7 on the interval [-6, -3].

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Q: Directions: Find the function f(t) given the following information: f"(t) = sin(t) + cos(t) f(t) =…

A: Given Function:- f''t=sint+cost

Q: R7 k=1 * x 3k

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Q: The units for f(x) are feet per minute (ft/min) and the units of x are feet (ft). What are the units…

A: The unit for f(x) is:  ft/minUnit of x is:  ft

Q: Question Use partial fractions to find the power series of -6 f(x) = (x²+4) (x²-2) Select the…

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Q: A particle is moving with acceleration a(t) = 18t + 14. its position at time t = 0 is s(0) velocity…

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Q: Suppose that the integral I = endpoints and n subintervals: 0 f(x) da can be represented by the…

A: Given  16-4n2·4n+16-8n2·4n+.....+16-4nn2·4n is a Riemann sum with n sub intervals for ∫0bf(x)dx We…

Q: Does the sequence {a} converge or diverge? Find the limit if the sequence is convergent. 8 ) (₁--/-)…

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Q: 5 1²+10x x² + 10x dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 26 85 k=1 087 (k+5)!

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Q: Calculate the work W done by the force F (x, y, z) = 7xi + yj - 2zk along the path r(t) = t³i+tªj +…

A: Given: F(x,y,z)=7xi∧+yj∧-2zk∧ r(t)=t5i∧+t4j∧+tk∧ Where, 0≤t≤2 Now, the work done W will be;…

Q: (81+st − zs)(1 — s) +8+ $T - $2 1-55

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Q: 4- Find the derivative of the function: g(x) = ₁ 19 Sin (12x) Cos(13x) 14√1+u² du.

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Q: 1. The position of a particle moving on a straight line is given by the function: S(t) = t3 - 6t2…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Use the Ratio Test or the Root Test to determine if the following series converges absolutely or…

A: We need to use the ratio test to test the convergence.

Q: 6. Using properties of definite integrals: Given the following, ff(x) dx = 8 and ₁³ f(x) dx = -1,…

A: Given:    ∫16fxdx=8     ∫13fxdx=-1 Using property:         ∫abfxdx=-∫bafxdx    ∫61fxdx=-8…

Q: Find the complete solution of (D² +1)y= sec (x) csc(x) using the method of Variation of Parameters.

A: We can find complete solution of the differential equations .

Q: A football is propelled straight up from ground level. Its height above the ground at time t is…

A: The height of football after time elapsed t is given.