04: Find x and y which satisfy the relation: -4 XZ ×-- ]

Q: Q.3// Solve the following second order differential equation: *+ 25x = 0

A: To solve the following second order differential equation. ẍ+25x=0

Q: Find the slope of the tangent line to polar curve r = Submit Question 5 sin at the point 5√3 T 2 3

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Q: 55. Show that 5₁²x -3 x-³ dx. 1 dx x³ +4 converges by comparing with

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Q: Find the average value gave of the function g on the given interval. 8 1+ t²' gave = g(t) = [0, 9]

A: The function isgt=81+t2 ; 0,9

Q: A semicircle of radius r=4x is inscribed in a rectangle so that the diameter of the semicircle is…

A: The radius of the semicircle is given by 4x To express the area of the rectangle in terms of x and…

Q: 9) There are $320 available to fence in a rectangular garden. One side of the garden is parallel to…

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Q: Find h'(t) given:h(t) = - 4.9t2

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Q: Consider the given vector field. F(x, y, z) = xyz i-x²y k (a) Find the curl of the vector field.…

A: Given vector field F( x , y , z ) = xyzi - x2yk

Q: 7) Answer the following: a. Find dy/dx where y = tan³ (5x) b. Find dy/dx where y = ln (5x+7)…

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Q: Find the 102nd term of: -8, -14, -20, ....

A: Solution

Q: 1. Use the precise definition of a limit to show that 12 lim x-3-x-3 8

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Q: Compute the work done by a force F(x, y) = V(x²+2x+y²) on an object displeed along a curve oining…

A: Workdone=∫F.⇀dr

Q: armer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Given vector v = (−4, 4), find 2.5v graphically by stretching the vector by its tip and then writing…

A: A given vector is v=<-4, 4>. We have to find the vector 2.5v graphically.

Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: To find the series is convergent or divergent if convergent  then find the sum of series.

Q: (1) (2) Find the points on the curve where you have a horizontal tangent line for the function…

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Q: Suppose the Maclaurin series fƒ(z) is ƒ(z) – Σ (³)*. = I

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Q: Number

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Q: A rock is dropped off the edge of a cliff and its distances (in feet) from the top of the cliff…

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Q: Solve for x: log₂ (2¹) --4 2

A: This is question of calculus Here one logerithmic equation given we have to solve for it. Further…

Q: ? Exercise 14.5.2 дz Az To calculate and for the following functions: Ju дv first calculate: Oz Ax…

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Q: Given the demand function D(p)=√125 - 4p, Find the Elasticity of Demand at a price of $30 At this…

A: D(P) = √(125-4P)  Find Elasticity of demand @ P=$30

Q: Find the length of the curve over the given interval. [0₁ r = 7, E|6

A: The given curve is: r=7  ;            θ∈0, π6

Q: Use the Limit Comparison Test for 4n² +9 n(n − 6)(n-14) ∞ Σ n=24 bn = an = an lim n→∞o bn M8 to…

A: The given series is (4n2+9)/[n(n-6)(n-14) ], n from 24 to infinity.

Q: (6) (a) Use three conditions of continuity to show that f(x)=√ is continuous over (7, ∞0). (b) What…

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Q: Find the area of the region. interior of r = 9+ sin(8)

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Q: 2 Solve the inequality f(x) <0, where f(x) = x²(x-4), by using the graph of the function. Q -~ EN…

A: To solve the following problem

Q: The graph of a function is given. Use the graph to find the indicated limit and function value, or…

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Q: •n [02/12 XP 3. an = P> 1

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Q: 7 fast ty → n T 1 4 N 3 13 What is the least possible degree of the polynomial graphed above?

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Q: Find the scalar and vector projections of b onto a. a=3i-j+4k, b=j+k

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Q: Find a formula of f-1, the inverse function of f. f(x) = (x² + 8)-¹, (-∞0,0] (Express numbers in…

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Q: A particle moves along a horizontal line. Its position on the line in t seconds is given by s(t) =…

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Q: Find the Taylor series at x = 0 for the function by calculating three derivatives and using the…

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Q: 10) The amount of infection exposed to the immune system by day t is given by: A(t) = f(f(s) ds…

A: Rate of change of something is derivative with respect to independent variable

Q: Find domain of y= log(4+4x)

A: Given  y= log(4+4x)   We need to find the domain.

Q: a. Compute the present value of an investment that generates income at a rate of 5000te 0.01 dollars…

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Q: Write an equation for the polynomial graphed below 4 y(x) = la 4- 3 373 a 8

A: The points at which the curve intersects or touches x-axis are zeros of the curve.

Q: Graph the following piecewise function, determine its range (use interval notation), and evaluate…

A: To graph the following piece-wise function, to determine its range,  and to evaluate f-3. fx=-4x+4,…

Q: Evaluate the limit. lim x→-4 x+5 x²+16x+64

A: given limit limx→-4x+5x2+16x+64

Q: A car is moving along a straight road. At time t seconds, the position of the car (in feet) is s(t)…

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Q: Find a Cartesian equation for the curve. r = 7 sec (0) Identify the curve. O circle O hyperbola O…

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Q: Evaluate the integral. Show that the substitution x = √14 sec (0) transforms I into cos(0) dº, and…

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Q: Evaluate 5 5 625 ** 4 Jo eys dydxdz.

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Q: Find the volume of the solid formed when the region bounded by the graph of f, the x-axis, and the…

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Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges.…

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Q: Find the general solution of the following dif- ferential equation: (x+t) da +x-t=0 dt

A: To find the general solution of the following differential equation. x+tdxdt+x-t=0

Q: 33. ∞ e√x dx 1 √x

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Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

A: Given: y=4+3x We are required to find: An inner function u=g(x) and an outer function y=f(u) such…

Q: a rate of r(t) = 6t^2 grams per minute. How much air is pumped into the balloon during the time from…

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