Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j O 31 10 O 3i

Q: 3dt 1. (8) +1 2t+

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Q: Suppose the position of a particle is given by parametric equations x(t) = t³-2 and y(t) = 5t2. %3D…

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Q: Write an equivalent exponential equation. 2 log 8 4= 3 The equivalent exponential equation is (Type…

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Q: Solve the differential equation. (x² + 15)y' = xy

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Q: 3) roțațion 90° counterclockwise about the origin

A: We know that,  90° counterclockwise rotation: (x,y) becomes        (-y,x)

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Q: Suppose the position of a particle is given by parametric equations x(t) = 2t2-1 and y(t) = 3t3. (a)…

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Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: (Rounded to the nearest hundredth) Use the cylindrical shell method to calculate the volume of the…

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Q: dy S4ト9-とト」

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Q: .2 xdx Evaluate (x²-2)5

A: Use simple integration formula.

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z? (4,…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 u · (v x w)| to determine…

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Q: After a rest of 20 minutes the hikers ascend into a steep climb, still following the trajectory of…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: is given by: If f(x, y) then 8(8x-4y) '

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Q: Answer

A: As per policy, only first question is answered.  Please refer to the image below

Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: The shaded region shown below is bounded by the functions f(x) = -4x? + 10 and g(x) = x + 6 and the…

A: area

Q: 11m Convert to its degree measure. 6.

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Q: 6. Determine, with reasons, the absolute maximum and absolute minimum of f(x) = x/2 – x on the…

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Q: (25-у? 5-х SŠ s *²+y²dzdxdy

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Q: Using Integration by parts, evaluate: ſ x³Vx³ + 1dx Your answer

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Q: 70 11 odometer. To find out how long this road is, you record the car's velocity at 10-second…

A: To find the length of the road, given velocity

Q: What is the reference angle of O if 0= -137°? A 43° B 47° C 137° D 223°

A: Given query is to find references angle.

Q: The edge of a cube is changing at the rate of 0.2 cm/sec. How fast is the volume of a cube changing…

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Q: Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Find the limit. lim V+3

A: Given query is to find the value of the limit.

Q: 22+88

A: The given data is: 22+88 To find the value of the sum.

Q: %3D What is the slope of the function y = 3x² + 5x – 7 at (-1,-

A: Given query is to find the slope of the function.

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

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Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Suppose the position of a particie is given by parametrc equations x(e) = -3 and y(t) = 2?. (a) Find…

A: The given data is: xt=t3-3yt=2t2  (a) To find the particle's position (x,y) at t=3

Q: 2x² + 1 Find the lim, f(x) where f(x) : if xs -5 x – 3x-2 if x > -5 x-5* -122/25 O -72/25 O -80 None…

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Q: Integrating Factor by Formulas: (4) (4xy + 3y² – x)dx + x(x + 2y)dy = 0 (5) y(x + y + 1)dx + x(x +…

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Q: The table below shows the velocity of an object.(cm/sec) at each sec as it moves along a track for…

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Q: Consider the parametric equations below. x = t? - 5, y = 3 - 4t, -3 sts4 (a) Sketch the curve by…

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Q: Choose the correct speed and direction of a plane with a velocity of (-5,12) . 13,293° 17,113°…

A: Find your answer below

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: Let f(5) = 6 and f' (x) <8 for all z between 5 and 16. Use the Mean Value Theorem to find the…

A: Mean Value theorem: If f(x) is a function that satisfies the followings.      (i) f(x)  is…

Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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Q: Find Ay and f'(x)Ax for y = f(x) = 6x, x =4, and Ax = 0.06.

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Q: Idx/(1-2x) = 1/2 In]1 -2x + C Select one: O True O False

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Q: Find the radius of convergence about x = -2 and interval of convergence of the series Sn°(ar + 2)"…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

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Q: tion Using Integration by parts, evaluate: S x³Vx3 + 1dx Your ancwor

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find out the directional derivative.

Q: 2, 22, 23 5 67 8 * 3. Test the series

A: Write the series as summation and use ratio test .

Q: Find two numbers whose difference is 40 and whose product is a minimum. (smaller number) (larger…

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