Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with the plane x = 2 at the point (2, 1, 3). (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:

Q: Using the RN approximation, express the area under the graph f(x) = 7 sin(x) over [0, €] as a limit.

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Q: ²-8 If f(x) = X-4' X = where is f not differentiable?

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Q: A closed rectangular box has volume 34 cm³. What are the lengths of the edges giving the minimum…

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Q: Calculate R5 for f(x) = 2x² + 9x over [-1, 1]. (Give an exact answer. Use symbolic notation and…

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Q: 4. Let f(x)= = x-1 x²-1' (i) State the domain of f. (ii) At which values of x does f have a…

A: Detailed solutions are given below.

Q: How can I find the height of a point off the ground, using the unit circle?  For example, the…

A: let's take a circle with the center 'O'. To find: - The height from the ground of the point P (x, y)…

Q: The graph of the curve x² + 5xy + 2y2 = 8 is shown to the right. (a) Use implicit differentiation to…

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Q: O (3³.3.32 + [23 [33 + Which shows the correct integration of 3.2² − +3•2+3In|2−1|]—[3³ + 2 3.3²…

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Q: Consider the differential equation dy dx The differential equation has an equilibrium solution at y…

A: To find the limit of the give function.

Q: Consider the differential equation:=-y. If the general solution is y = cet ,cER, which one of the…

A: We can solve this as follows:

Q: Let ƒ(x) = 4x + 3x². Compute the difference quotient f(x + h) − f(x) h and simplify it so that it…

A: Here we have to find the value of 'c'.

Q: determine the open intervals on which the graph of the function is concave upward or concave…

A: Given query is to find the interval where function is concave up and down.

Q: >) Sketch the graph of a possible function / that satisfies each condition: f(0) = 3 f(3) = 0 f is…

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

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Q: Let f(x) = ln(2e + 3). Then f-¹(x) equals None of the above 2/ln(e* - 3) In(e* - 3) In(e* - 3) In…

A: Note: Since, the student has posted two questions but the second question is incomplete. So, we are…

Q: Sketch a possible graph of a function that satisfies the conditions below. f(0) = 1; lim f(x)= 3;…

A: Topic = Function Correct graph =D

Q: The area under the curve y = 2.5-3.5 and above the z-axis between z = 3 and 2 = 10 is: area The area…

A: Given curve equation:- y=2.5x-3.5

Q: A lab rat is escaping, and its position is given by f(t).  Once f(t) is greater than or equal to 5…

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Q: QUESTION 4 Evaluate the expression. (f. g)(-2) when f(x) = -2x + 3 and g(x) = -8x² + 5x + 6. O-15…

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Q: Most fish can adjust to a change in the water temperature of up to 18 degrees Fahrenheit if the…

A: Introduction: An absolute value inequality is an inequality that has an absolute value sign with a…

Q: A contour map for a function f is shown. Estimate the value of f(3, 14) 20 15 10- 5+ 70 f,(3, 14) 10…

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Q: Use technology to sketch the level curve of f(x, y) = 4x - 2y + 9 that passes through P(1, 2) and…

A: Given: f(x, y)=4x-2y+9 Level curve passes through point P(1,2). The gradient vector at P=?

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given…

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Q: How did you divide the interval into 5 parts?

A: Our aim is to explain how to divide the interval -1, 1 into 5 sub intervals of equal length.

Q: Find All Solutions 1+ cos x = sin a on the interval [0,2π)

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Q: Find an appropriate parametrization for the given piecewise-smooth curve in R³. x² + y² 4 16 C(t) =…

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Q: Let f(x) = [2x +9 if x 2 Determine whether f(x) is continuous at x = 2. If f(x) is not continuous,…

A: Given query is to find function is continuous at x = 2 or not.

Q: Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use…

A: Given Graph:-

Q: Suppose f = 200x¹y and fy 200x¹y and fy = Make use of two antiderivatives f(x, y) = 160x5y³ +…

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Q: The graph below is the function f(x) -5 -4 -3 -2 -1 3 2 1 lim f(x) = 2 f(2)= lim f(x) lim f(x)= 1…

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Q: Write the augmented matrix of the system and use it to solve the system. If the system has an…

A: Concept: The Gauss Jordan Elimination, also known as the Gaussian Elimination, is a method for…

Q: f(x)=-5x+4 g(x)=x²+x Find a) (f+g)(x)=? domain of f+g : ? b) (f•g)(x)=? domain of f•g : ?

A: We have given two functions  fx=-5x+4 gx=x2+x (a) f+gx=fx+gx f+gx=-5x+4+x2+x f+gx=x2-4x+4 Domain is…

Q: Find the horizontal and vertical asymptotes of f(x). 3x X+4 f(x) =

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Q: Consider f(x) = x² + 6x + 7

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Q: The graph of f is given. State the numbers at which f is not differentiable. x = (smaller value)…

A: The graph of f is given. To state the numbers at which f is not differentiable.

Q: QUESTION 2 Write an inequality of the form |x-a k so that the inequality has the given solution…

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Q: Find y'' for y = 4+ 5X 3

A: Given :   y=4+5x3     To Find : y''

Q: For the given functions f and g, find the requested function and state its do f(x) = x-9; g(x) = 9x²…

A: Given query is to find indicated function and it's domain.

Q: Evaluate the sum. 34 2 (7) + 4/1²) 7j 3 j=2

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Q: Find dy dt = dy dt - for y = cos 2 (4nt – 7).

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Q: Estimate the integral 1-1 + (2) dx by using appropriate Simpson's rule in dx. which the function y =…

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Q: If sinx+cos x = 1/3, then 18 sin² X -9|=

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Q: Consider the ODE: "-7y" -/+7y=0. Which one of the following is the general solution to this ODE?…

A: The given differential equation is: y'''-7y''-y'+7y=0 So, we can also write as: D3-7D2-D+7y=0   The…

Q: Solve the differential equation (x² + y²)dx − 2xydy = 0.

A: Given differential equation ( x2 + y2 )dx - 2xydy = 0

Q: QUESTION 13 Use the horizontal line test to determine whether the function is one-to-one. -10 00 No…

A: In a horizontal line test we draw lines parallel to x axis on the XY plane on which the graph of the…

Q: lim z0 In(2x + 7) - In(7) H

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Q: -3 8.5 -0 TH -$ 4 € 7 1 19- 1 M P La

A: From graph, In left side , graph is increasing.    Maximum value of f is is infinity.

Q: 720 Consider the function f(x) = 5x + on the interval [8, 15]. Find the absolute extrema for the…

A: Answer: 1) Given function F(x)= 5x+720x on interval [8,15] We have to find Absolute maxima and…

Q: Consider the following differential equation, To solve this differential equation, we must first use…

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Q: By expressing (") and (, "₁) i in terms of factorials, show that () + (₁²₁) = (^#¹).

A: nr+nr-1=n+1r by expressing nrand nr-1 in terms of factorials.