Find a value a > 0 so that the graph of the exponential function f(x) = a" contains the point (3, 1/27). a

Q: 9. Sketch the solid obtained by rotating the region underneath the graph of the function f(x) = Vx2 ...

A: The answer is in step 2.

Q: Solve for the Linear Differential Equation: y' + y = 1

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Q: Consider the region bounded by x = 1+ 4y – y? and x = 4. a. Compute for the end points of the region...

A: (a) computing the end pointintersection point between x=1+4y-y2 and x=44=1+4y-y2y2-4y+3=0y2-3y-y+3=0...

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A: The x-intercept is where a graph crosses the x-axis and the y-intercept is where a graph crosses the...

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = square root...

A: This is a problem related to find area of the curve using integration. Please use below method to so...

Q: xdx Evaluate Vx-16 Vx2+16) +. Vx2-16 + C A. In In +C C. In In ) x-16 x--16 в. In In + C D. In In + C...

A: Given

Q: Find the third term of: E33-1)n+1 (z+3)2n (2п)! Σ n=D

A: This is a problem related to series expansion and calculating the term of it. Since series is starti...

Q: Find the critical number and relative extreme if they exist.

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Q: 2. Suppose g(2) = 8 and g(5) = 512. (a) Write an equation for g(x) assuming it is linear. (b) Write ...

A: Given query is to find the equation for g(x) for linear and exponential modal.

Q: Find the length of the curve y = In (1 – 2*) over the interval [-,].

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Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at ...

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Q: Use Disk Method or Washer Method (for all parts) to set up an integral (without the absolute values)...

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Q: Determination of Integrating Factors : Solve the equation y (4x + y) dx – 2 (x² – y) dy = 0 2x2 - xy...

A: We have to find the Integral factor and solve the equation. 

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

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

Q: 3. Let f(x) = 1+x + x² + x³ + xª + x5. (a) ) Pind T3(x), the Taylor polynomial of f at x = 0 with de...

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Q: (ii) Solve x(2z - 3y)p + y(3x + z)q + yz + 2xz = 0

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Q: Find the area of the region bounded by y = x^2- 5x + 6, the x axis, and the vert çal lines x = 0 and...

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (0,...

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Q: A statement S, about the positive integers is given below. Write statements S,, S2, and S3, and veri...

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Q: In how many ways can you place 9 different books on a shelf if there is space enough for only 5 book...

A: Given, 9 different books on a shelf and there is space only for 5 books. 

Q: 2 A = -4 1 6. has an eigenvalue A of multiplicity 2 with corresponding eigenvector v. Find A and X =...

A: Given     Matrix is given

Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 26, (1, ...

A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.   x2 + ...

Q: Find the area of the parallelogram that has u = 1 v = 3j+ k as adjacent sides. NOTE: Enter the exact...

A: Given query is to find the area of the parallelogram.

Q: 3. Solve for fe)(r) given that f(r)% = sinh(3r)

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Q: Suppose that f and g are integrable and that f (x) dx : :-1 | f(x). h(x) dx = 4 Odx = 5 Use the rule...

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Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of ...

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Q: Scos x vsin x dx (sin x)i-(sinx) +C (sin x)i +(sinx)+c c. (sinx)- (sinx) + C (sinx)i +(sinx)+c A. B....

A: ∫cos3xsinxdx  

Q: A first order linear differential equation is one that can be put in the form +P(z)y=Q(z) where P an...

A: xdydx-y=-2x7+12x4

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Mini...

A: This is a problem of maxima and minima. Based on the general formula we will find out the value.

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx = -(1+2x)...

Q: For the demand function q =D(x) = 100 find the following. a) The elasticity b) The elasticity at x 7...

A: Given q=D(x) =100) x

Q: Problem Solving 1. Determine f(x) given that f'(x) = t* – t3 + t² +t – 1

A: Taking integrate on both side. 

Q: 4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of pol...

A:

Q: Writing a Definite Integral In Exercises 15-26, write a definite integral that represents the area o...

A: topic - definite integral

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a din...

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number o...

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: We will draw the vector and will compute required vectors as follows 

Q: 27 at z = 0. Find the equation of the tangent line to the graph of y(z) = Equation of the tangent li...

A: Find the equation of tangent line to the graph of y= 2x/√(1-x2) at x=0 . 

Q: Figure 2: The three faces are labeled - including the third 'outer face'. If there are no areas encl...

A:

Q: 04: Show that y = 35x - 30x +3 satisfies (1-x)-2+20y = 0 da

A: We have to show y=35x4-30x2+3 satisfies 1-x2d2ydx2-2xdydx+20y=0

Q: x cos x + sin x Find x sin x *xp-

A: Evaluate the following.    ∫xcos(x)+sin(x)xsin(x) dx

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x...

A:

Q: Apply your understanding of vector operations to simplify the following algebraically: 3(u+v)−3(u−v...

A: Given query is to simplify the expression.

Q: A tank is filled with 1000 liters of pure water. Brine containing 0.05 kg of salt per liter enters t...

A:

Q: Express the sum using summation notation. Use the lower limit of summation given and k for the index...

A: We have to calculate summation

Q: Evaluate ſ xe3x dx A. (1/9)(3e³x – e³) + C B. (1/9)(3e³x + e3x) +C c. (1/9)(3xe3x – e3x) + C D. (1/9...

A: Integration by parts:∫u(x)v(x)dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Compute the volume bounded by y=x2-2x and 3y + 2x?-27 = O when it ís revolved around the y-azis. A. ...

A: Note: According to our expert guidelines only first individual question is to be answered.kindly rep...

Q: Graph the function and find its average value over the given interval. a. g(x) = -|x| on [-1,0] b. f...

A: The objective is to graph the functions and find its average value over the given interval.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r ...

A:

Q: S dx Evaluate: А. п B. VT c. VT3 в. D. еп A B C D

A: