the

Q: Sketch the region enclosed by the given curves. Draw the approximating rectangle, label its height…

A: see below the figure of the region and rectangles that can be construct in the region.

Q: Sketch the region bounded by the curves y=x², y =0, x=2 and find the exact coordinates of the…

A:

Q: Using the graph given below, state the value of f(3). y 4 2 0 2 4 If the value does not exist, enter…

A: Given the graph of a function

Q: 21. If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f'(1).

A: Topic - functions and derivatives We are given , f(x)+x2[f(x)]3=10  and f(1)=2We know…

Q: 5-8 The graph of a function f is shown. Does f satisfy the hypotheses of the Mean Value Theorem on…

A:

Q: Find the volume V of the solid formed by rotating the region inside the first quadrant enclosed by y…

A: Given that Curve y=x3 and  y= 25xand Rotation about x-axis.Solution :

Q: A population of bacteria grows to twice its original amount in 3 hours. How long will it take to…

A:

Q: Find Angle between two vectors b = (4, 5, 2). Let à (5, 1, — 4) and = Find the angle between the…

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Q: 39-52 (a) Find the intervals of increase or decrease. (b) Find the local maximum and minimum values.…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: If x² + y² + z² = 9, dz dt = dx Š dt dy dt = 4, and = 3, find dz dt when (x, y, z) = (2, 2, 1).

A: x2+y2+z2=9 dxdt=4 and dydt=3 (x,y,z)=(2,2,1)   Differentiate the given function with respect to t:…

Q: Solve the initial value problem y" + 4y + 4y = 32e²; y(0)=-1, y'(0) = 14. +Set →→ (Answer: Y =…

A:

Q: Solve y" + 2y' - 3y = 1 + xex O y = C1e^-3x + C2e^-x + (1/8)x^2 e^x - (1/16)xe^x - 1/3 O y = C1e^-3x…

A:

Q: Given the position function s(t) = 2+³ - 2 +² - 60++ 3₂ where it is in seconds and s is in ft, Find…

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Q: For the position function s(t)= - 16t² + 113t, complete the table shown below with the appropriate…

A: The given data is: st=-16t2+113t Complete the given table with the appropriate average velocity.

Q: Sketch the region enclosed by the given curves and find its area: y = √√x-1, x−y=1.

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Q: what is the derivative of the inner function?

A: We have to tell the derivative of inner function

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x² - 6xy + y² +…

A: f(x,y ) = x2 - 6xy +y2+16y +3  First we will find critical poits by partial derivative and putting…

Q: If h(x) = f(g(x)) and f(1) = 7, f'(1) = 10, g(1) = 1, and g'(1) = -5, find h''(1).   a) -50 b)…

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Q: Jse logarithmic differentiation to find the derivative of the f 3x y =(√x) ³x ''(x) =

A: We need to find out the differentiation of the function.

Q: Scientists can determine the age of ancient objects by the method of radiocarbon dating. The…

A: given half life thalf life = 5730 years      law of decay x = x0e-ktk = constant x = radioactivity…

Q: Find the absolute minimum of f(x, y) = 5xy - 4x - 4y on the triangular region R that has vertices…

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Q: If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the…

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

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Q: Write Equations of a Line in Space Find the point at which the line 7 (t) = (1, 3, 8) + t( − 2, 5,…

A: Given form of line is r→t=1,3,8+t-2,5,6 We need to find the point where the given line intersect xz…

Q: Finally, f(x) = 5(x2-9). Practice Give an expression for f(x) using only Real-valued coefficients,…

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Q: Find the derivative of: 9 sin² ( − 4xº). 1 Hint: sin²(x) = [sin(x)]²... 9 cos cos²(-429) -36x8 ...so…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Write the equation: Vertical asymptote at x = −1, double zero at x = 2, y-intercept at (0, 2)

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Q: Consider the function f(x) = x² − 72x² + 5, −5 ≤ x ≤ 13. This function has an absolute minimum value…

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Q: Find the general solution to the given equation 2y" + y − 3y = 0

A: The objective of the question is evaluate the given differential equations.

Q: Find Vectors and Perform Vector Operations in R³ Vector 7=(2, 0, − 1) has initial point (-9, 7, 3).…

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Q: Consider the following figure. To -6 -5 -4 -3 -2 -1 11+ 10+ 9+ 8- 7+ 5 5+ 4- لیا 3- 2+ 1- O -1+ 2 N=…

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Q: Write the particular solution of the first order linear differential equation (1 + x)dy + (y - cosx)…

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Q: Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least…

A: To write the equation of polynomial.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = surface x =…

A:

Q: 0.12 200e

A:

Q: For the given function, identify any critical points, and use the second derivative test to…

A: Given function: fx,y=1-4y2+5x-12

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x³ X y y 1 x…

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Q: Find Cross Product Let à = (3, – 3, — 4) and 6 = ( − 2, – 3, 5). Find à x 6. V

A: Given query is to find indicated cross product.

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given vector:- rt=2ti+etj+e-tk

Q: Find the following using the table below. x 1 f(x) 3 f'(x) 2 2 3 4 2 4 1 4 1 3 g(x) 4 3 1 2 g'(x) 2…

A: Given that hx=fx.gxh'x=f'x.gx+fx.g'xh'2=f'2.g2+f2.g'2h'2=4×3+2×3h'2=12+6h'2=18

Q: Determine the higher-order derivatives of a function of two variables. Given f(x, y) = x - 5xy³ +…

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Q: Which one of the following could be the graph of the polar function r = 1 + 2 sin ? 1. 013 2. P…

A:

Q: Problem 5. Consider the curves y = 4x, y = 1/x and y = 1. (a) (b) Graph all the curves to visualize…

A: Let's graph the given curves and find area of region.

Q: A cereal company find that the number of people who will buy one of its products the first month it…

A:

Q: Find the PS for (x²y" + 2xy' - 12y = 0 y(1) = 1 y'(1) = −1

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

Q: y = cot (4x) dy dx Find dy dx =

A:

Q: For a certain automobile, M(x)=-015x² +1.43x-7.6, 30s x s60, represents the miles per gallon…

A: Given, M(x)=-.015x2+1.43x-7.6

Q: 4 Let f(x)=x²-3x-2380, x>0.75. Find the value of df-1 At x = 0, dx (Type an exact answer in…

A: Given function:- fx=x4-3x-2380

Q: B. At what rate the probability of de- veloping cancer increase with solar ex- posure

A: Given P(x)=e-2+x+3x21+e-2+x+3x2

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Given query is to find integral converging or diverging.