find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

Q: (-2, 39) -4 10 20 10 10 -20 89 -30 1 (14) (27) 23 Solve the following problems. A. Given the graph…

A: Given ,  Graph of function (4) We have to tell local minimum value

Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

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Q: 4. Find the member of the curve whose slope at any point is and passes through the point (3, 4)

A: Given slope (m) = 3x/4y Passing through a point (3,4) Therefore member of the curve whose slope…

Q: Find the derivative of the function at På in the direction of u. x-y g(x,y) = xy+2¹ Po(1,-1),…

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Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² x 10

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Q: 1. Graph the function below Using Calculus, find the intervals where the function increases and…

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Q: Q: find the cartesian equation of the plane Containing the point p(2.1.1) and parallel to the plane…

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Q: 0 Convert the following polar equations to Cartesian form and identify its graph. a.) r = 2 (3 cos +…

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: dw For the functions w= -5x² + y², x = cost, and y = sint, express as a function of t, both by using…

A: Given query is to find the Indicated derivative.

Q: Find the binommal coefficient (4)

A: Topic = Algebra

Q: 2) Given the vectors a-[4, 2, -6], b-[6, -3, 2], and c-[-5, 0, 4], simplify the following vector…

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x-axis and below y = 4 - x² b.…

A: Let's find  area between given curve and x axis.

Q: Determine if the series converges or diverges (2) La=2 ਪੰਜਾ

A: To determine whether the given series converges or diverges.∑n=2∞ 4n3

Q: 2. (a) | +4 Evaluate the integral. √2x + 1 dx

A: Taking substitution as 2x+1 = t

Q: 9.) Find all horizontal and vertical asymptotes of f(x) = 4x 5 - x² - 9

A: The given function is f(x)=4x-5x2-9 First we factorize the numerator and the denominator.…

Q: Evaluate the definite integral. 8 (2n-²-n-³) dn 8 (2n-²-n-³) dn=[ 4 (Type an integer or a simplified…

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Q: Find the gradient of the function f(x,y)=5y-x at the point (8,9). Then sketch the gradient and the…

A: See this solution in below

Q: Evaluate the following integrals: 0 (Cartesian to Polar) Given the cartesian coordinate, find FOUR…

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Q: 1. Evaluate the given integral Q. Q • S S (² (x - y) dx dy -

A: Evaluating the given integral

Q: η3+n2 (5) Σ=o (n+1)!

A: Series ∑n=0∞ n3+n2n+1!

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic - trigonometric ratios and application of derivatives

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

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Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Let P be the population after t years

Q: Find a power series representation for the function and determine the interval of convergence. (Give…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: 10.) Solve. Write the exact solution in terms of logarithms. el-3x = 4

A: This question can be solved using the concept of natural logarithm.

Q: center of the mass of a thin density covering the Constant density 8. by the x-axis and EA Y = 3/2/…

A: We have been given that curve  y =32cosx with -π3 ≤x≤π3                  and   density…

Q: Convert each pair of rectangular coordinates to polar coordinates where r>0 and 0 ≤ 0 <2. 1) (-3,0)…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 6 and x = -4 x intercepts…

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Q: * Use Cramer's rule to solve the equation X +y +z 2x -y 3x +2y -z ↑ Add file || || || 1 4 -3

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Q: Two capacitors with capacitance of 6 μF and 4 μF are connected in series across a 100 V dc source.…

A: Question- Two capacitors with capacitance of 6 μF and   4 μF are connected in series across a 100 V…

Q: Problem 2. Consider the equation z = x² + y² + 1 A. Find the equations for az- and yz-traces. B.…

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Q: Use differentials to approximate the value of (1.02)².

A: Given :y=(1.02)2

Q: he point  P(8, −3)  lies on the curve  y = 3/(7 − x). (a) If Q is the point  (x, 3/(7 − x)),  use…

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Q: . Find the integral of your answer in problems 2a and 2b.

A: 2. Write the given (total) area as an integral. Given problem:- a. The area above the x-axis and…

Q: A drag racer accelerates at a(t) = 96 ft/s2. Assume that v(0) = 0 and s(0) = 0. a. Determine the…

A: To find out the distance/position function.

Q: Consider the letters A, B, C, D, E, F, and G. give the number of different arrangements or…

A: Here given that 7 different latter    Now the 1 latter can be arrange any of 7 letters  Choice of 1…

Q: integral e^u du = e^u+ C. Is it true or false

A: Given query is to find statement is true or false.

Q: 6+ З +2 (2x+1)= 8

A: 6x3 + 2(2x+1) = 8 2x + 4x + 2 = 86x + 2 = 86x = 8 - 26x = 6x = 66 = 1

Q: Given R(t) = 4 costi + (1+ 3cost)j +5sintk. Find T(t). T(t) = -sin ti -sintj + costk Option 1 3 4 5…

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Q: Assuming that z is a differentiable function of x and y, Let F(x,y,z) = ln(x²y) - e* -tan-¹ z. Find…

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Q: Find the area between (bounded) by the Curves y=x² +10x and y= 2x + 9°

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Q: 3x 4. Find the member of the curve whose slope at any point is and passes through the 4y

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Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: 1. Evaluate the given integral Q. JR (y - 2x) dA, R where R is the region bounded by x = 0, y = x, x…

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Q: Compute the center of mass/ centroid of the region R = {(x, y): 1≤x≤3, 0≤ y ≤ x²

A: Here we have to find the centre of mass of a region.

Q: Let g be a function such that g'(x) = x (x - 3). Complete the following arguments to get all…

A: Given, g'(x) = x(x-3) We have to find the extrema from the second derivative test.

Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

A: