Find an equation of the tangent plane to the surface at the given point. x² + y² - 5z² = 108, (-7,-8, 1)

Q: Find the general solution in the form y = yc + yp. y'' + 4y' + 5y = e-2tcost

A: y'' + 4y' + 5y = e-2tcost Find genral solution

Q: Graph the trigonometric function. sec Start by drawing three consecutive asymptotes. Then plot two…

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Q: dy dx sin(xy) = y dy dx Find the = given the equation

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Q: Two runners are in a 16-mile race. Runner A runs at a constant speed of 8 miles per hour, while…

A: Topic- Mean value theorem We are given, distance of a race= 16 mile speed of runner A=8 miles per…

Q: 3π Find the area of the sector of a circle with diameter 36 feet and an angle of radians. 5 Round…

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Q: Find ay dt + = -1 (+-√e ³ sin ¹ (2+) 1(5+2log +) 9

A: We will use the formula ddtmn=nm'-mn'n2

Q: ************** A cylindrical package to be sent by a postal service can have a maximum combined…

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Q: y² Consider the paraboloid f(x,y)=4- and the point P(6,0) on the level curve f(x,y) = 0. Compute the…

A: I am attaching image so that you understand each and every step.

Q: 4. Suppose that the following equation defines y as a differentiable function of x: 2√y + y = 2x.…

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Q: Evaluate f"(x) when x = π/4 if f(x) = sin(x)cos(x)

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Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

A: limx, y→0, 0xy2x2+y4along path x=0=lim0, y→0, 00· y202+y4=lim0, y→0, 00=0along path x=y2=limy2,…

Q: Given the following functions, find each: 2 f(x) = x² - 9x + 18 g(x) = x - 3 (f + g)(x) (f - g)(x) =

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Q: 11. Refer to the figure and find the volume generated by rotating the given region abou specified…

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Q: Find using properties of logarithms: y = ln (= cos(z)) 36x-1 dy d

A: We can find the derivative using the properties of logarithms in in the below steps.

Q: The dye dilution method is used to measure cardiac output with 4 mg of dye. The dye concentrations,…

A: Given ct=29te-0.6t, 0≤t≤10 Quantity of dye is 4 mg

Q: Find f'(x) using the QUOTIENT RULE if f(x) = 6-x² 3+x² f'(x) =. Find f'(4). f'(4) =

A: I am attaching image so that you understand each and every step.

Q: 4 Find the derivative of f(x) = x¹ log7(x + 4.5). f'(x) =

A: Given that f(x)=x4log7(x+4.5) Differentiating with respect to x…

Q: nd the equation of the tangent line to the curve y = (cotx) at x = 1.

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Q: Subject: Differential Equations Yoon Se-Ri is baking a cake for Captain Ri Jeong-Hyeok in a kitchen…

A: Concept: We have given the room temperature 76.81°F Cake temperature is given 420°F  also after…

Q: Find the gradient of the function at the given point. Function Point f(x, y) (7,3) Vf(7, 3) = 15 2 x…

A: Please see the below picture for detailed solution.

Q: 1. 2. * Your answer is incorrect. Solve the initial value problem y" - 5y36y = 0, y(0) = a, y'(0) =…

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Q: Use any method to evaluate the integral. S 243 dw w²√√81-w² 243 dw w²√√81-w² W (Type an exact…

A: Given data:- ∫243w281-w2 dw

Q: Find the first and second derivates of the functions. h(t) = t^4 - 7t^3 + 5t^2 - 8t - 14…

A: Find the first and second derivative of the function

Q: F(g) = √ 39 29 2-g if g≤0, tang if 970,

A: Given data, The function is continuous at g= 0. Determine if it is differentiable at g = 0.…

Q: 9. Evaluate the definite integral, L'xa x(1-x)¹82dx

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Q: 1. Let f(t) represent the amount of sea level rise, in mm, above mean sea level, where t represents…

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Q: Let t be the number of days since concert tickets went on sale. The daily sales function is 110t 50+…

A: We need to find tickets sold.

Q: In each case, determine whether or not the lines have a single point of intersection. If they do,…

A: Part_a_ r1=5t, 2t-1, 2t-2 and r2=t-7, -t+6, t-9   First rewrite both the equation in different…

Q: Find the third derivative of the given function. g(t) = √9t + 3 _g"(t) = X

A: We need to find out the triple derivative for the function given.

Q: Let g and h be functions defined by g(x) = 2× · f(x) and h(x)=3x² + 4x-In√x. Part A: Find g'(8).…

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Q: (4) Explain why fx ln x dx is improper. Evaluate it using the limit of a proper integral.

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Q: 3. Find a particular solution Y(t) of y" — 2y" — y' + 2y = e²t

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Q: Question Evaluate the integral. So 70 Give an exact answer. If the integral is divergent, enter Ø.…

A: We will find the required integral.

Q: ASK YOUR TEACHER A rectangular package to be sent by a postal service can have a maximum combined…

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Q: = 5x² + 3x + xy = 5 and y(5): = 27, find y' (5) by implicit differentiation.

A: Given query is to find the derivative at indicated point.

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

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Q: Graph f(x)=3* and g(x) = log 3x in the same rectangular coordinate system.

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Q: (b) Is the function f(x)=z+z+1| continuous at every z? Is it differentiable at every z? Sketch the…

A: Explanation of the answer is as follows

Q: 2. Given Q(x) = 27x³ +1. a) b) c) Show (3x+1) is a factor of Q(x). Factorize Q(x) completely into…

A: Given Qx=27x3+1

Q: Sunset Lake is stocked with 2000 rainbow trout and after 1 year the population has grown to 5200.…

A: I am attaching image so that you understand each and every step.

Q: Let f be defined as follows. y = f(x) = x² - 7x (a) Find the average rate of change of y with…

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Q: The circumference of a sphere was measured to be 89 cm with a possible error of 0.5 cm. Use linear…

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Q: Find the degree 2 Taylor polynomial, P₂(x), for the function f(x) = (3x + 8)4/3 centered at x = 0.…

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Q: Prove the identity. tan (+) 2 tan (7) + cos(x) tan (+) = sin(x) 1 - cos(x) X + cos(x) tan (-) = = X…

A: To prove the following identity.tanx2+cosx tanx2=sinx

Q: If f(x) = ln(x) where x = [1, 3] is rotated about the x-axis, then the area of the resulting surface…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…

Q: It is known that f(-5) = 15, f'(-5) = 10, 15, f''(-5): JAN f(³) (-5) = 5, and f(4) (-5) = -2. Find…

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Q: Determine if the following matrix is in reduced form. If not, indicate the row operation(s)…

A: In reduced form of matrix, every row should have 1 as it's first non zero element.

Q: Consider the ODE (a) The general solution y(t) of the corresponding homogenous ODE is Yh(t) Osin(at)…

A: NOTE: Refresh your page if you can't see any equations. . the given DE is

Q: Let sin 3x сos 13лу = sin 3x + cos 13Ty = T(x) of the tangent line at (0, 2), then evaluate T(13).…

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Q: 5. Suppose the derivative of a function f is f'(x) = (x - 2)²(x + 1)³(x − 8)¹. a) Find the regions…

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