1) Suppose a ball is dropped from a window 20 feet above the ground. a) Find the height of the ball after 1 second. b) Find the velocity of the ball after 1 second. c) When will the ball hit the ground? What is its speed at that moment?

Q: Find the indicated quantities for y = f(x) = 4x². f(1 + Ax)-f(1) Ax (A) Simplify (B) What does the…

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Q: Evaluate the integral. 6 [°₁ (x² + 2x (x² + 2x - 7) dx

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Q: Find the absolute maximum and minimum of f(x, y) = 1x + 2y within the domain x² + y² ≤ 5 1. Absolute…

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Q: Question What is lim q(x)? x→0+ q(x) = 6 X COS 2 (x + 7/1)

A: q(x) = (6/x)-(2/cos(x+π/2))  We have to find lim x->0+  q(x)

Q: Evaluate 567 12 If F(x, f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: x² + y² = 9, 0≤x≤ 3, 0≤zs X

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Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 3³. Express r as a…

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Q: Given that tan(8) = 1.13, match each of the trigonometric functions with their value. sec(8) cos(8)…

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Q: Suppose that f(x, y) = 4x + 4y at which {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4} D Then the double integral…

A: The given function is: f(x, y)=4x+4yD= (x, y) | 1≤x≤2,  x2≤y≤4

Q: The part of the surface z = 4 + 3x + 2y2 that lies above the triangle with vertices (0, 0), (0, 1),…

A: To find the area of the surface that lies above the triangle with vertices (0,0), (0,1) ,(2,1)

Q: A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost…

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Q: If r(t) is the position vector of a particle in the plane at time t, find the acceleration vector.…

A: given,  r(t)=(6cost)i+(3sint)j

Q: 1.Find all the first partial derivatives of each function a. f(x,y)=e* b. f(x,y)=√x² - y²

A: *Note – when finding the partial derivative w.r.t on variable, other variable consider as constant.…

Q: Find the length of the curve r(t) = = (5 cos (5t), 5 sin(5t), 4t) for 0 ≤ t ≤9 Give your answer to…

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Q: The gradient of f(x, y) = e³zsin(1- y) at (x, y) = (2, 2) is defined as followed: V f(x, y) =…

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Q: Use Green's Theorem to evaluate [F. Tids, where F = (√x + 3y, 2x + 3y) C is the boundary of the…

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Q: Find the equation of the line perpendicular to the line 3x + 5y = -9, through the point (-1,4). y-4…

A: The equation of the given line is 3x+5y=-9 The point through which the perpendicular line passes x0,…

Q: Question Given (-6 (-62⁰ - 42³ + 5x – 3)dx, evaluate the indefinite integral. Do not include +C' in…

A: Given    ∫(-6x6-4x5+5x -3)dx   We need to integrate this.

Q: nd an equation for the line tangent to the curve at the point defined by the Py at this point.…

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Q: 4.Describe the largest set S on which it is correct to say that f is continuous b. f(x,y)=(1+x² +…

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Q: Evaluate the surface integral. √ (z + x²y) ds S is the part of the cylinder y² + z² = 4 that lies…

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Q: f(x, y) = V 2 2 3x² + 4y²

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Q: Find if the series converges and if it does and you can find the sum, find it: 3. Σ0 (0)

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Q: CS Find the length of the curve r(t) = (5 cos(3t), 5 sin(3t), 4t) for -2 ≤ t ≤ 5 Give your answer to…

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Q: Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤t≤3 Calculator ·[F. Check Answer F. dr…

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Q: 2.) = x³ - 6x² +9x+2. Find the relative minimum/maximum, on · g(x) = x³ - 6₂ what interval is…

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Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) 3. Express r as a function…

A: Given the volume of a sphere is 150 cubic feet.

Q: Find the principal unit normal vector N for the curve r(t). r(t) = (8 sin t)i + (8 cost)j + 8k

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Q: tan(0) Rewrite the expression esc(0)sec (0) in terms of one trigonometric function. Show your work…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy)…

A: Function is  f(x,y)= 4x sin(xy)  Point is (1,5)

Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional and at the…

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Q: FIAT -T IF a Sequence C₁, C2, C3,... has limit k then the sequence e, é²², c²s, has limite C. C2…

A: an = (1+33/n)^n

Q: Solve the problem. 16) Determine the dimensions of the rectangle of largest area that can be…

A: Given, The dimension of the rectangle of the largest area can be inscribed in a semicircle of radius…

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. 0 T -f²v…

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Q: I Suppose that f(x, y) = at which {(x, y) | 3 ≤ x ≤ 5,2 ≤ y ≤5}. y D Then the double integral of…

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Q: If r(t) = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ and fr(t) dt= with C a constant vector. i+…

A: r(t)=cos(-3t) i+ Sin(-3t) j-10tk

Q: 2. Find the area of the curve of r =2cose in the interval [3] ·]. 2 (Remember 2cos²x=cos2x+1)

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Q: Solve indefinite integral with steps: sin5x*cos((2x)/5)

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Q: Find the limit lim (z,y) → (0,0) 13x7 + sin y 7x7+y7 along two different paths.

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.…

A: logba=logkalogkb

Q: Find the directional derivative of the function f(x, y) = ln (x³ + y) at the point (-2, 2) in the…

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Q: Find the points on the cone z² = x² + y² that are closest to the point (5,2,0)

A: Given data: The cone z2 = x2 + y2 Point (5,2,0)

Q: 1.) f(x) = x³ -27x +46 Find relative minimum and maximum points and any critical values.

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Q: Find the mass of a lamina bounded by y = 3√x, x = 9, and y = 0 with the density function o(x, y) = x…

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Q: The gradient of f(x, y) = e²´ª sin(2 · y) at (x, y) = ( − 2, − 1) is defined as followed: V f(x, y)…

A: Given the function and its gradient at (-2,-1).

Q: The parametric form of the tangent line to the image of f(t) = (3t², ½, t + 1) at t = 5 is L(t) =

A: We have the parametric form of the tangent line to the image of f(t)

Q: Evaluate 567 12 √f F(x, f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: x² + y² = 9, 0≤x≤ 3, 0≤z≤x X

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Q: Find [ady + yda, where is the arc of the curve y = e² for 0 ≤ x ≤ 2

A: The given arc is:y=ex   for    0≤x≤2

Q: The matrices D and F are defined as follows. P-(419) -- () D= F Carry out the indicated matrix…

A: The given matrices are;  D=( 1 4 0     F=(2 1       -1 3 2)         1 3                           4…

Q: Determine if the sequence converges or diverges. I it converges, give the value. 2. {an} = {5 -…

A: Determine if the sequence converges or diverges. If it converges, give the value.  {an}= {5-1/n}