f(x, y) = R is the rectangle bounded by +1 -5

Q: Let f(x)=x^3-2x^2-4x+104 on the interval [0,3]. A. Find all crirical numbers of F(x) inside [0,3]…

A: We have to calculate absolute maximum and minimum.

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim Xn inf {xn :…

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Q: 4. Find y' * 2 (x – y)² = sin x + sin y

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Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

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Q: 1 Suppose that L is a location function of an object, given as L(t) = We will compute the 3t – 2…

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Q: Questio The population, in thousands, in a given city is modeled by the function P(t) = 100.2(1.04)…

A: This is a problem related to power function. Based on the general concept and formula we will solve…

Q: Solve the following differential equations: (DE in 1st Order, 2nd Degree) 7.) (v')² +| x – 2x y'+x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: ar +b. 2r' - 1, f(z) = I>3

A: The given function,fx=ax+b,x≤32x-1,x>3

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Scalar Projection of AP on AB is defined as AP→.AB→AB→

Q: Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

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Q: Solve the exponential equation by using the property that b^x= b^y implies x=y, for b>0 and b≠1.…

A: Given query is to find the value of x.

Q: Solve the differential equation with appropriate method. Finalize answer equated to y. dy/dx = (-5x…

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: 1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of…

A: a) ∫-12x2-3xdx=x33-3x22-12=233-3(2)22-(-1)33-3(-1)22=83-6+13+32=-32∫-12(x2-3x)dx=-32b)…

Q: Evaluate the following integral using the method of partial fraction. (2х3-3х?) dx a. 2x2-7x+5

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Q: Solve the attached integral problem

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Q: one-sided limit (if it exists). 72. lim

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Q: An object hangs from a spring balance. The balance registers 36 N in air, 25 N when this object is…

A: given

Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

A: Given problem:- Find an equation of the plane that passes through the point P(-8, -4,7) and has the…

Q: Rung-kutta ylsx+zy use o Sulve me hou2s

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Q: 11) The Inverse of ()= *-1* a)(x) 3x-1 b)/(x) log2(x) d)f(x)= log3(Vx+1) e) non

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

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Q: Solve the given third-order differential equation by variation of parameters. у" - бу" — у'+ бу 3D…

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Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows

Q: Y2 = Find the area bounded by these curves. (All choices are in sq. units) Y1 = Vx + 3 (x+3) Y2 = 2

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Q: S sin x In(cos x) dx

A: Given problem:- ∫ sin(x) ln(cos(x) dx

Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of…

A: Here, De can be written as: y''+14x2y=0⇒P(x)=0, y1=x12ln(x)

Q: 7. Approximate (22 + 3) dz using four rectangles and the left endpoint method.

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Q: Please solve the problem using the Substitution Method. Thank you!

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Q: Find the area bounded by these curves. (All choices are in sq. units) Y1 = sin z Y2 =

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Q: How can the area be negative?? This is incorrect! Please correct the answer!

A: Apologies for the inconvenience. Last line was a mistake.    Step 3: Line 2 of the original solution…

Q: The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial point:…

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Q: (29.4) Determine whether the series (-1)"-1. n2 + 1 is absolutely convergent, condi- n=1 tionally…

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Q: Show that for x 2 1, cosh (cosh° 3x – sinh° 3x) = In(x+Vx² -1). (b)

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Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: find of the f llowing 2. 2 -5x*

A: Solution of question is written in below steps.

Q: (a) Oppositely directed to v = (3, -4) and half the length of v. %3D W3= (?, ?) (b) Length V5 and…

A: To Find : a) A vector which is oppositely directed to v=<3,-4> and half the length of vb) A…

Q: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

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Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

Q: Find the sum of positive divisor  a)     40 425  b)       2 491

A: To find the sum of the positive divisor a)     40425 b)      2491

Q: Consider the function y= x³ – 9x + 4. a. Sketch the graph of y= x3 - 9x + 4. b. Find and describe…

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Q: X Your answer is incorrect. Find an equation of the plane that passes through the points (-2, 1, 1),…

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Q: Find an equation of the plane satisfying the given conditions.

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Q: Pls show the complete solution, thank you very

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Q: 8. Find the volume of the solid generated by revolving the region bounded by the curve y = 4 – x²…

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Q: АCTIVITY GIVEN : 2x 2x 1 2х + 3 1 f (x) = 1 –x 8 g(x) = 3(x + + 4 h(x) = 6 a.lim -4 · f (x) d.lim (8…

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Q: 2. S(r2 +r + 1)e"dr 3. Find the area of the region in th

A: Given problem:- ∫ (r2+r+1)er dr

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.