A force of 30 N compresses a spring 0.3 meters from ita natural length of 15 meters. Find the spring constant k. Oa 25 Ob. 100 Oc. 0.3 Od -25 O. None of the choices.

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A: From the given graph

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

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Q: 6. The definition of the first derivative is f(x+h)+f(x) E. f'(x) = F. f'(x) h f(x+h)-f(x) h…

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Q: s representation for f(x) 1+ x3 ° find the exact the power series obtained 2.

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Q: Set-up the integral for the area A(R) of the region R bounded by the circles y2 + x² = 4, and y2 +…

A: Region bounded by two circle in fourth quadrant

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Q: Demand for The Secret Loves of John O, a romance novel by Margó Dufón that flopped after two weeks…

A: Let's find.

Q: 5. In antidifferentiation, the formula § x" dx + Cis valid if? %3D (n+1) А. nER В. п# 1,п€ R С. п€…

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Q: Evaluate the definite integral. el" i+ej+t k)dt O el7 i - e- j+ 17 k O el7 1 i- (e-- – 1) j + , k…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y2…

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Q: O (1, 5) О (-о, 1.5] O (-1, 4) О (-3, 2)

A: Let's find.

Q: The monthly profit, P(x), of a company is expected to change at the rate of 6,498 P' (x) = 3 (2а —…

A: THE SOLUTION IS GIVEN BELOW

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Q: Find the directional derivative of the function at P in the direction of f(x, y, z) = xy + yz + xz,…

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Q: I need help with all of these problems

A: Given

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Q: (Show your solution) Compute the inverse of the function f defined by f(x) V+ 2. Determine the…

A: We have to calculate inverse of a function  And the domain and range of the inverse function.

Q: Which of the following series is convergent? 00 (-1) 4. n=1 O None of them. 00 2(-1) 6. n=1 00 6. 11…

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Q: 2x e3a² dx

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Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (4, -3, 5), v = (0, 6, 4) (a) u: V (b) u.u (c)…

A: I am attaching image so that you understand each and every step.

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

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Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Solve the differential equation dy y(0) = -1. dx 3+1 There is no need to isolate y.

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Q: Question 2 Let f: (ry. ry) and g:= (cos(t), sin(t)). Then determine the following. (a) fog.

A: This is a problem related to combined function. Based on the general concepts and formula we will…

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Volume

Q: Determine whether the geometric (– 1)"3" series * is convergent or divergent, n=1 8" and if it is…

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Q: solve the following differential equations using the substitution suggested by the equation.

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Q: 1. In the differential equation (x+2y-1)dx+(2x+4y-3dy -0, we let the substitution

A: In the differential equation (x+2y-1)dx+(2x+4y-3)dy=0. we let the substitution W=?

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y. (4, 0,…

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Q: Rojana is 8 years older than AJ, and the sum of their ages is less than 24. Find their possible…

A: We will find the possible age of Rojana and AJ in the following step.

Q: Let f be a continuous function. Show that 2022 f(1/a) dx f(x) dz. %3D 1/2022

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Q: 2. Given {-t,-n St< 0. f(t) = {t, 0stsa f(t) = f(t + 2n) (i) Sketch the function for 3 cycles. (ii)…

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Q: In the differential equation (1 + 3x sin y)dx - x2 cos ydy = 0 , we let the substitution w =…

A: Solve the following

Q: (- 1)" Σ n =1 n 3+5 8.

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Q: A tin can has a base diameter of 10 cm and a height of 10 cm. The can is initially full, but a hole…

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Q: Find the gradient of the function at the given point. g(x, y) = 13xeY/x, (5,0) Vg(5, 0) =

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: The given sequence,i) an=6-(0.9)n ii) an=n36n3+1

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: In how many different ways can 7 potted plants be arranged in a row with 5 spaces? O 720 O 2 520 5…

A: There are total 7 potted plantsThere are 5 spaces in a rowNumber of ways  to arrange 7 potted plants…

Q: 1. S V2x – x² dx 2. S* dx 1+x? 1+x3 3. Sv1+ v1+x dx 4. Set up only the integral(s) that will compute…

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Q: Find the integrals of the following function. 1. Se3xdx 2. S(e3x + 1)?dx

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Q: Use the comparison test to verify that the following serie 00 1 Σ n=17+n7

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Q: Find the area of the region that is enclosed by the cardiod r = 16 + 16 sin 0. %3D

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Q: 5. x3 + 2x – 6 dx x4 + 2x2

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Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

Q: r = - 10i + (1 – 1² )j + t k O It is a parabola in the plane z = – 10, with vertex at (1, 0, – 10),…

A: Find your answer below

Q: pien x = p sin p cos 0, y = p sin p sin 0, z = p cos p д(х, у, 2) a(p, 8, 4)

A: