f(x) = 9x² - 4 at x = 1

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

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Q: Q4) Find the largest eigen value for the matrix A= 54 with x (0)=(7/17 1)

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Q: Find the value of the following implicit derivative tan y-sec x=5 find...y'

A: Given problem :- Find the value of the following implicit derivative   tan(y)-sec(x) = 5 find   y'

Q: Determine whether the following function is differentiable at x = 9 f(x)=√x²-16, x<9 √x, x ≥9 (a)…

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Q: 5. Solve the equation = 170. 6. Solve the following logarithmic equations. (a) log, (+5) = log, 3…

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Q: Which of the following equations does not represent an ellipse? * x² + 2y² - 16 = 0 Option 1 x² +…

A: topic - equation of ellipse

Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: 1. Determine y(t) if y(0)-0. dy +5 selt- ydt + 2y = 10 What is the value of y(t) in question #1 if…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose…

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Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Solve for the general solution of (ylny-e^-(xy))dx+(1/y+xlny)dy=0

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Q: solve the differential equation 2) 2x² dy dx csc (X)

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Q: The proper way to evaluate f (3 + h) for the function f(x) = −4x² + 3x − 1 is Of(3+h)=(−4(3)² + 3(3)…

A: We can answer the question as below.

Q: What are the rectangular coordinates of the point whose spherical coordinates are (1,,)? x = 0 y = z…

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Q: 3s - 8 4s² +25 3 COS (²) - 2 sin (²) Option 1 O None of the Choices 3 25 sin Option 5 8 COS sin…

A: This is a problem related to inverse laplace transform. Based on the general formula and concept we…

Q: Let f(x) = x²30 Find the critical points c that correspond to local minima.

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Q: The graph shown is the 1st derivative of function where its domain is 20 10 8 2

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Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

A: Given: curves y=x^2+10x , y=2x+9 We have to find the area between the curves

Q: Evaluate the characteristic w "+k²x ²³w = 0 value of k in the following differential equation w…

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Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: Solution 1 y = (x +3)(2x – 5) y = 2x² + 6x - 5x - 15 y = 2x2 + x - 15 y = 2(2x)2−1+1-0 y' = 4x+1…

A: Please see the below picture for detailed solution.

Q: (a f (x) + b g(x)) '= a f (x) + b g'(x)

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Q: Given the following functions: Find: f(j(x)) f(x) = 3x² - 5x+2 g(x) = 7x² + 3x - 1 2x - 7 h(x) 5x -…

A: Given query is to find the Indicated composite function.

Q: 7) Find the critical point (s) of f(x, y) = 2x³ + 3y² - 9x² - 30y + 12x-3. Then use the second…

A: solution is given below...

Q: A smooth vector-valued function R(t) satisfies R(1) = (-3,7,9), R'(1) = (0,5,6) and R'(1) = (4, 1,…

A: Explanation of the answer is as follows

Q: . In each part, find polar coordinates satisfying the state conditions for the point whose…

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Q: 3. LL₁a+ (x + 2y) dy dx

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Q: 7. (10 pts) Evaluate the integral Sa x4 6x5 - 1dx

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Q: Find the general solution of the following linear first-order ODE (1-x²)y' +2y-x=2

A: We need to solve D.E.

Q: dy dt t •S 0 +5 ydt + 2y = 10

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Q: 1-12 Find the area of the surface. 1. The part of the plane x + 2y + 3z = 1 that lies inside the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: If u = x² tan equal to (a) (c) x - y x + y - 2 + V² 2 X X -, y x + y x - y x² + y² 2 X - y - y² tan…

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Q: 1. If F(x) = Le d ex dt, find F(1) and F'(x).

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Q: 5. 2 Let f(x) = 5x4. +8√x - 3. x² (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: x-1 x-1+√√2x-x²-1 Evaluate lim

A: Please refer to the image below

Q: S tan-1 е' 1+4t² 2t dt

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Q: Consider the circular helix with equation R(t) = (12t, 5 cost, -5 sint). (a) Find the value of t…

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Q: In 2000, an investment was opened with an initial deposit of $1800. The investment had grown to…

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Q: 2. Evaluate: 0 √|2 − x + x dx

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Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: We know that for some real number k, the function 3ekx is the solution of the second- order…

A: This question can be solved by substituting the value of y in the given differential equation.

Q: y=x² - 4x and y=-x²+2x.

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Q: A spherical tank of diameter 6 m is full of water. Find the work done in pumping all the content to…

A: Follow the procedure given below.

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: b) Find the cube roots of 27%. Leave your answer in polar form. c) Let z3 = 1+√√3i. Write z3 in…

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Q: s 1 s(s+ 1)² -1 +et+2te-t Option 1 2+te-t Option 3 - 1 + e-t2te-t Option 2 -2+te+e-t Option 4

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Q: Find the area of the region bounded by the graph y = sin x, y = 0, x = 0 and x =3π/2

A: Area of a region when strip taken parallel to y-axis is ∬dydx.

Q: 2x lim x-0 x²+5x

A: The given limit,      limx→02xx2+5x