At what point on the ellipsoid x² + y² + 4z² = 1 is the tangent plane parallel to the plane x + 2y + z = 1? smaller x-value larger x-value (x, y, z) = (x, y, z) =

Q: Consider the function f(x) = 2x² √11 -x on the interval [7, 15]. Find the absolute extrema for the…

A: Introduction: If f has an absolute maximum on I at c or an absolute minimum on interval I at c, we…

Q: Evaluate the following limit using the Change of Variable technique: lim x-27 x-27 √√x-3)

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Q: f(x)=-3x(x+2)^3(x+4) im stuck on how to find the zeros of the function and their multiplicities

A: INTRODUCTION The multiplicities of a function, or the number of times the function crosses the…

Q: for the graph of 2x² - 6x, when is the slope -8

A: Given query is to find the points where slope of -8.

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 4x - 4x…

A: Note: Since in the question it is mentioned to solve parts (a) through (d), but the student has…

Q: let f(x)=2x-1, and g(x)=x+1 find f(g(x))=? O 2(x+1)-1 2x+2 2x O none of the above

A: To find the composite function

Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

A: Given,           Suppose an arrow is shot upward on the moon with a velocity of 42 m/s, then its…

Q: Let f and g be differentiable functions. Find a general formula for the derivative of y = f(x)9(x).

A: Given y = f( x )g( x )

Q: K OYes 4 2- Yes ++ Graph 4 4 2 -20 O NO 2 2 ONO X X -8-64-2 O Yes -8-6 -4 4- 2+ -24 4+ 8- Graph 5 4-…

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Q: d(A. B) dt = A. dB dt dA dt B

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Q: X f(x) = {x² + 2x 1 at a = 0 if x = 0 if x = 0

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Q: - 110 1 I 9

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Q: 3. (a) For P(t) = (4t² + 3) (2t³ — t)¹², find P'(t). After taking the derivative(s), do not simplify…

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Q: ne cost of producing x units is given by C(x) = 21294 + 1.1x + 14x² dollars. Find the value of x…

A: Given query is to find the value of x , which gives minimum average cost.

Q: Evaluate the integral from 2 to 3 of  dx/((x^2)-1)^(3/2)

A: Given integral is ∫23dx(x2-1)32

Q: Find the derivative of the function using the definition of derivative. g(x) = √5 + 4x g'(x) = State…

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Q: Find lim h→0 lim h→0 f(3+h)-f(3) h f(3+h)-f(3) h || - if f(x)=x² +2. (Simplify your answer.)

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Q: Find (f+g)(x)=? Domain of f+g is ? Find (f•g)(x)=

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Q: Find the distance in between the point P(−1, −2, 2) and the point Q(3, −1,0).

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Q: Find the following limit." lim x →4 x3-8x2+20x-16 x-4

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Answer: The solution is given below:

Q: 2. Consider the function: f (x) = 64x² +9 Step 1. Find the critical values of the function. Separate…

A: Given function:- fx=64x2+9x

Q: Solve S 1 (4x² - 9) ³/2 dx using trig sub and solve

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Q: [ƒ(3x) dx = 29. If f is a continuous function and F'(x) = f(x) for all x, then f(3x) dx = 1 O (A)…

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the equation of the line tangent to the graph of f(x)=−x2−x+4 at x=−1.

A: The given function fx=-x2-x+4. We have to find the tangent line at x=-1.

Q: Graph the line with slope 1 and passing trought -1,-5

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Q: 1.) Find the equation of the tangent & normal line to the graph of y = √x-1 at the point (3,2). f…

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Q: The second order linear differential equation that has y = 3er as a solution is: y'= (a) y" - 4y +…

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Q: 2. Find the equation of the tangent line to y = x² + 2 at x = -2.

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Q: 2. Find the limit of the following functions f. lim x →∞0 x5 - 3x + 1 x-5

A: The given limit is: limx→∞x5-3x+1x-5

Q: 19. Let f be the function defined by ƒ(x) = √√| 4 − x | for all x. Which of the following statements…

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…

Q: 5 -4 -3 -2 -1 5 4 3 2 1 5c= دها -2 234 -4 1 2 3 4 Find the components of the vector 5c based on the…

A: Solution: According to the graph c→=<-4i, 3j>

Q: stimate f′(6) where f(x)=x^3−4x^2−20x−5 to within one decimal place by using a small enough…

A: given that f(x)=x3-4x2-20x-5then we have to find value of f'(6)

Q: -3x The area of the region between the graph of y= e³x and the x-axis for x ≥ 2 is е

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Let (a) Find lim f(x) #0+ = 7 sin(x) I +5c 3x6 #≤0 (b) Find the value of c if f(x) is continuous at…

A: Here we have to use the concept of the limit

Q: 24. If f is a differentiable function such that f(0) = -4 and f(5) = 5, then which of the following…

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Q: Is the function (x² - 1)/(x - 1) continuous at x = 1? Answer this question by evaluating f(1) and…

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Q: Determine the value of k so thatf(x)is continuous at x = 2. 2 k² - x², x < 2 f(x): = 1.5kx, x ≥ 2

A: here we have to find the value of "k".

Q: dy Solve = dx 2-y 2-x

A: To solve the given differential equation

Q: explain how you arrive the answer

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Q: hat is the value of c if (1 + c) = 4 and c> 0? n=1 nswer: c =

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

Q: The graph of y = f(x) (solid) and y = g(x) (dashed) is shown --6 -5 -4 Find the following limits.…

A: Given query is to find indicated limit.

Q: Use the graph of the function f shown to estimate the following limits and the function value.…

A: By using the graph of the function f shown ro estimate the following limits and the function…

Q: s is given by h(t) = 49t - 0.83t². Find the average velocity over the given time intervals. 3,3.5]

A: we are asked to find the average velocity

Q: Using the graph of f below, determine what type of discontinuity does f have at the given numbers.…

A: There are several types of discontinuities, including: Jump Discontinuity: A function has a jump…

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x² + 4y² − 2x − 8y + 1, D…

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Q: Suppose an arrow is shot upward on the moon with a velocity of 49 m/s, then its height in meters…

A: It is known that velocity is defined as the rate of change of hieght function

Q: 4. Determine the value of k so that f(x) is continuous at x = 2. 2 k² - x², x < 2 f(x) = 1.5kx, x ≥…

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Q: Write each equation in sta opening of the parabola. y=2x^(2)-24x+40

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