Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+ 7tk; t= 2 NOTE: Enter the exact, simplified answers. K = p =

Q: Write the expression as a single Integral 1. f f(x)dx + f(x)dx =, 2. S f(x)dx – , f(x)dx = 3. f…

A: Use the property of the definite integral; 1). ∫abfxdx=-∫bafxdx 2). ∫acfxdx=∫abfxdx+∫bcfxdx   1).…

Q: Solve for x in the following expression using the quadratic formula. 3x2 + 19x – 4.9 = 0 Use at…

A: We can solve this as follows:

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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Q: The graphs of the function f (r) = 7 - a and g(a) = 3 are given below. %3D

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Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: -2+0.5-0.125+...= (Write your final answer in fraction form, when applicable)

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Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: Solve the logarithmic equation algebraically. Approximate the result to three decimal 8+ 7ln x = 14…

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Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: Find the first derivative, show all your work i(x)=2^{-0.8x+35.032}

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Q: A swimming pool is circular with a diameter of 40 feet. Depth is constant along east-west lines and…

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Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: A small resort is situated on an island that lies exactly 4 miles from PP, the nearest point to the…

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Q: stimate using the trapezoid rule and Simpson's rule for et dx;n3D8 -2x+5

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Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: 3 + In?x dx

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Q: ex-e-* Find Maclaurin series for: 1. sinh x = 2

A: Find your answer below

Q: (

A: We will find the centroid of the triangle.

Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: i 15Y4 + 32X+ 23x?+ 25X-3

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Find the directional derivative of the function

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Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

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Q: 4 fy 1 -3 -2 1 -1 -2

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Q: Write the expression as a single Integral -3 1. Sf f(x)dx + S, f(x)dx = -3 - 3. S f(x)dx + S, f(x)dx…

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Q: Solve the inequality involving absolute value. |x-3|/4<2

A: Given :        x-34&lt;2

Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: For a plane curve r(t) = (x(t), y(t)), |æ'(t)y" (t) – x"(t)y' (t)| (x'(t)² + y' (t)²)³/2 - k(t) Use…

A: Here we have to use this equation to compute the curvature at the given point.

Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: 4r-10 (2r+2hlx-3-thb+20+C (2 + 2hk-3 +4hk+ 2) +C Option 1 Option 2 (भे+ 22 + 210l2 3/ 4Mly /2) 1 ८…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = t'i + t°j

A: Here we have r(t)=t2i+t5j We have to find κ(t)=r'(t)×r''(t)r'(t)3 ..................................…

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: Improper integral: If f(x) is not continuous at x=c where a&lt;c&lt;b and ∫ac f(x) dx and ∫cb f(x)…

Q: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below

Q: Evaluate the line integral / -ydx + xdy along the curve C C : y? = 27x from (27, 27) to (0,0). NOTE:…

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Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: Diego knows that 82 64 and that 4° = 64. What other statements are true? O V64 = 8 O V64 = 4 O…

A: We can find the true  statements as below.

Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

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Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

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Q: f(b) - fla)

A: We have to choose the correct option from the given options according to the given information

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: Find the indefinite integral and check the result by differentiating. Determine an appropriate…

A: Solve the given intregal