39. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Az and dz.

Q: 3x lim The limit 2 x-2 (see graph) is

A: Here, to find the given limit: limx→2+3xx-2

Q: 2-Vn n=1

A: Here, the given series is: ∑n=1∞2-n=∑n=1∞12n=∑n=1∞12n2 which is a positive term series for all n.

Q: Ve dx

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Q: S sec*x csc*x dx

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Q: Find the solution of the given initial value problem. cos t y%3D t 1 y' y(T) = 0, t >0 - t-1 y(t)

A: The given equation is; y'-y/t =cost/t-1; y(π)=0.

Q: 21. Determine the general antiderivative of f(x) = 4x 4x4 + 9 2x2 a. 2 cosh +C 3 22 + C c. 2 sinh¯ -...

A: As per our guideline we are supposed to be answer only one question you can repost other question in...

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion...

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Q: 7. Determine which of these positive integers are a) 1,5,7,11,13,17,19,21, 23,25, 29,31 b) 1,5, 7,11...

A: We know that  Two numbers are said to be relatively prime if their greatest common divisor is one. F...

Q: Calculate the left Riemann sum for the given function over the given interval using the given value ...

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Q: аx2а (х2а+1)* dх ax²a

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Q: 4. Given that r(t) = cos ti + sin tj + In cos tk Find the curvature k and vec- tors T, N, B at the g...

A: Find curvature at t=1

Q: In the arguments bebu, vymboline both the givens and the a full two column prove statemunt. Then, wr...

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Q: The temperature, in degrees Celsius, at a point (x,y) on a metal plate is given by T(x,y) = 20-4x^2 ...

A: Given Temperature on a metal plate at point (x,y)T(x,y)=20-4x2-y2

Q: dy find dx t - 1 If y = t and æ = t+1 dy A. 2t(t + 1)2 dx В. dy = t(t+1)² dx dy 2t С. dx (t + 1)? dy...

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Q: For vectors ū = (1,-5,2) and v = (3, 1,-4), calculate the following: a) ū• i b) the angle between ū ...

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Q: Use logarithmic differentiation to find the derivative of the following: 8. h(x) = 25x34x² ans. h'(x...

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Q: You are inflating a spherical balloon at the rate of 7 cm³/sec. How fast is it radius increasing whe...

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Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this...

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Q: Direction: solve and analyze each of the following problem in neat and orderly manner. Do this in yo...

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to t...

A: Since u denotes the temperature of an object, dudt ∝ (u - ua)dudt = - k (u - ua)(Negative sign impli...

Q: 12. Let F (x, y) : that = esin x+cosy (cos x,– sin y) and C = {(x, y): x² + y² 0. Show [ F- dR = 0 ...

A: Here we will use the Stroke's Theorem to prove the result.

Q: 2. State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state whethe...

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Q: f(2) Suppose that the limit value of: lim a , what does imply? g() O a. A limit exist. O b. The nume...

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Q: Find the direction cosines of the vector v = (2, –4, 4) %3D

A: The given vector v→=2,-4,4

Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y = 9...

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Q: A trough is 40 ft long and has semicircular ends, with the flat side facing up. The semicircles have...

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Q: The number of bacteria "N" present in a culture increases at a rate proportional to the number prese...

A: Topic:- function

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3. (...

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the functi...

Q: Differentiate the following functions. Show step by step solution and Indicate your final answer. y ...

A: A detailed solution is given below 

Q: sinr f(x)=(x)'

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Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

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Q: When a bullet is fired into a sand bank, its retardation is assumed equal to the square root of its ...

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Q: Evaluate the expression lim, v3r+ 8. a. 2/5

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Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: y(x^2+xy-2y^2)dx+x(3y^2-xy-x^2)dy=0 solve using homogeneous equations

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Q: Suppose Gavriel's utility depends on the amount of time spent playing on Xbox (X) and the amount of ...

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Q: Determine (without solving the problem) an interval in which th solution of the given initial value ...

A: 16-t2y'+5ty=7t2 , y(-7)=1 ⇒dydt+5t(16-t2)y=7t216-t2 16-t2=0⇒ t2=16⇒ t =±4  

Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. (1+9) 6. an = %3...

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Q: (2xy+y^2)dx-2x^2dy=0 when y=e and x=e solve using homogeneous equations

A: Given (2xy + y²) dx - 2x² dy = 0.   With x = e , y = e To find Particular solution of Homogeneous D....

Q: x²dx x³+ 4 3.

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Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x ...

A: Based on x and y intercept value we will find out equation of the graph. 

Q: Usin IVT how do you show this equation has a root. On the interval (0,2)

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Q: Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in the direction a.  o...

A: 4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in the direction a. ...

Q: dy The following problem involves an equation of the form dt = f(y). Sketch the graph of f(y) versus...

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Q: [2x+5y=7 3x + 2y = -6' 1. Solve the linear system using graphical method.

A: The given linear system,2x+5y=73x+2y=-6

Q: Answer the question below: The student should find the local linear approximation of a function in t...

A: Let's find. 

Q: Use implicit differentiation to find the derivative y' of the following: y²+2ye2x у?е2x + хуз — 1%3D...

A: Given :6. y2e2x+xy3-1=07. xey+3y-10x=0To find: Implicit differentiation to the derivative y'.  

Q: 3. Express the quadratic function g(x)=-4x² +4x+5 in the form a(x-h)' +k by completing the square, a...

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Q: A. Find the derivative of the given function at a given number 1. y 3x-2 at f'(1) *Derivative of Alg...

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x = (Use symbolic notation and fr...

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