Differentiate r(t) = (cos(t)², sin(t)², t³).

Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: Let g(x) = 2x² - 216x. Find the relative maximum and minimum values of g. Also find the intervals on…

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Q: Estimate f (5.06) for f as in the figure. y=f(x)/ ƒ (5.06) ≈ (4,2) (10,4) Tangent line X (Give your…

A: The figure is given as,Estimate

Q: If what does the following integral equal? 4 19 q(s)ds = [ q(s)ds = 13 and La q(s)ds = 10.7

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Q: ind the limit if it exists. lim (12x+11) elect the correct choice below and, if necessary, fill in…

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Q: For the functions f(x)=x^2-6x+10 and g(x)=5, determine the following information. Vertex of…

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: Solve the following initial-value problem: dy dx = e sin x 2xy e cos x + x² y(0)=0

A: Given differential equation

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: 3. Given that w = xyz + y² + x + 1, x = et, y = 82, 2=t+1. ) Find Ow/as. (b) (c) Find 0w/Ot. Find…

A: Given that .(a) To find .(b) To find .(c) To find .Note: Since the student has posted many sub-parts…

Q: b.Let f(x)=x²-3x² -1, x ≥ 2. Find the value of af dx at x = -1.

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Q: Find the absolute extrema (max and min) of f(x,y)=3x^2-2y^2 over the disc x^2+y^2<=1. Indicate all…

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Q: For y = f(x) = 7x³, find f(x₁+Ax)-f(x₁) Ax f(x₁ +Ax) -f(x₁) Ax -, given x₁ = 5 and Ax= 3.

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Q: Baseball A (square) baseball diamond has sides that are 90 feet long (see figure). A player running…

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Q: For what values of a and b does lim x→0 a = b = sin (2x) x³ +a+ b 2/2) = x² = 0?

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Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: +² dt F(x) In(t) F(x), determine whether F is inc a dec x>2 at x=2020

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Q: 1. Solve dy_3-x-y x + y €1 dx 11

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Q: Let f(x, y) = x sin(x + y) (a) Calculate the directional derivative of f at the point (1,-1) in the…

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Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: Evaluate the following limit. lim x³e -x² xxx = Note: Input DNE, infinity, and -infinity for does…

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Q: Find the domain of the function. f(x)= x-1 X+2

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Q: e,f,g

A: By using previous solution sign Table xf'(x)Positive zeroNegativeDNENegativezeroPositive

Q: Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers.…

A: The given polynomial function is  on the interval .

Q: Suppose f (x, y) =x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6, 1) y…

A: The tangent to a curve at a point is obtained by finding the slope at that particular point using…

Q: Find the lines that are tangent to the curve y = 2tan(pi*x/4) at x=1

A: The equation of tangent line passes through point  with slope

Q: Find the direction cosines and angles of u and show that cos²a + cos² ß + cos² y = 1. (Round your…

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Q: An = (3″ + 5n)1/n

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Q: Use the Gauss-Seidel iterative method to solve the following system of equations. Remember to show…

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Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: 5 4 --3- 2 -1

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Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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Q: Evaluate the double integral [[ (zy + 2) dA, where D is the set of points contain within the corner…

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Q: Evaluate the integral by converting to polar coordinates. 2 √8-y2 S² S Y 1 √1+x² + y² dx dy= = 16pi

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: (a) Consider the curve y = e dx 6x + 6). (c) This function is always differentiable. Its derivative…

A: Consider the curve (a) To find (c) To find the values of  when .(d) To find the intervals where the…

Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of…

A: Please solve the given problem using the concept of derivatives.

Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

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Q: The total cost (in dollars) of producing x food processors is C(x)=2300+60x-0.3x². (A) Find the…

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Q: Let g(x)-3x³-20x² Find the relative maximum and minimum values of g. Also find the intervals on…

A: The given function is

Q: S Write an equation for a line parallel to y y = -4x + 4 and passing through the point (4,-2

A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: 2.21 A mathematical model describing the state of a learner y(t) at time t while learning a specific…

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Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ''(x)(x − b)dx a

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Q: Consider the equation below. f(x) = 4x³ + 9x² - 54x + 1 (a) Find the intervals on which f is…

A: In this question, we will find the interval of increasing and decreasing.

Q: In 1994, the moose population in a park was measured to be 4460. By 1997, the population was…

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