Question 5 The improper integral +∞0 5+0⁰ 0 ex dx is

Q: Evaluate the definite integral by substitution: 21 1 dx 3/(1+3r)² (1) ² 3/1 + 13xdx 10 (3) [TV. (3)…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x) = x + 1. A unit² 3 B -unit² ©…

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Q: dx x²√x² + 1 2 18. 1

A: Use substitution method for solving this integral.

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Q: Using disk method, find the volume of the solid generated by revolving the R bounded by y = 3(2 − x)…

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Q: Verify that 2+ ?х ду 2+ дудх : for f(x, y) = 2x³y6 – 4x5y4.

A: Partial differential.

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Q: Write a linear cost function for the situation. Identify all variables used. A parking garage…

A: Given query is to find the cost function.

Q: A lighthouse is on an island 350 meters east of the shore of Lake Bella. The lighthouse beam makes a…

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Q: Evaluate the double integral: 2 √² √ (3x² +9y²) dxdy A 40 B 30 C 60 D 80

A: Double Integration by iteration:

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: ร n=1 6 : 2n-1 3h

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Q: Find and sketch the domain of the function. f(x,y)=√y-x-8 Find the domain of the function. Express…

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Q: Find the general solution of the given system. dx - 2x + 3y dt dy dt - 6x + 5y Ex(t), y(t)) 0

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Q: tretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.

Q: o find 224 ах ду and 224 ду ах' we must first find af af and ?x ду

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Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² ® unit² Ⓒunit² 1 D unit²

A: topic - area bounded by curves

Q: Let g(x)=6x-4. Find g (Type an integer or a fraction.)

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: y= (sec ³x + tan ²x)

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: |x-4|dx

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Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

Q: A balloon is released fromthe ground 100 meters from an observer.The balloon rises directly upward…

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Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: A company selling widgets has found that the number of items sold, x, depends upon the price, p at…

A: Given ,  A company selling widgets has found that the number of items sold , x , depends upon the…

Q: (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

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Q: ff. W Ex] Let f(x) = 4x²+2x²+x+3 and :f(x), g(x) € 75[x] f(x). g(x). g(x) = 3x² + 3x²³² + 3x² + x…

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Q: 1.30 Find the value of the integral ₁00 √x dx by using simpson method (n = 6)? 1.00

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Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: C option is false.

Q: The sum of two numbers is k. Find the minimum value of the sum of their squares.

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Q: R is the region bounded by the functions f(x) = 1 - 3 cos (x) and g(x) = 4 sin (x). Find the area of…

A: Ans : A=12 unit2

Q: -1/2 Find the gradient of f(x,y,z) = (x² + y² +2²) −1/² + In (xyz) at the point (1,2,2). Vfl…

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Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x = 3. A (e²-1)² e2 sq. units (e²+ 1)² e2 (e³-1)²…

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Q: The region is bounded by y = x² - 9 and y = x + 3, find the area.

A: Solve the following

Q: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: First we diagram the problem, labeling the point A , the lighthouse beam as B and C as another…

Q: e: Sz dx (x+1) log(x+1)

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x = 3. (A) (e³-1)² e3 sq. units B (e³+ 1)2 e3 (C)…

A: To find the area bounded by curves

Q: Determine whether the correspondence is a function. Domain Range 1 22 20 7 7 6 Is this…

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Q: 10. Given the curve C defined by the vector-valued function r(t) = a) find an equation of the line…

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Q: x y 1 x 2 y' equal with x(5)=6

A: Given query is to find the solution of the differential equation.

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: If fx and gx are integrable on the closed interval a, b, and k is a constant, then to determine wich…

Q: What is the equation of a line with a slope of 5 and passing through the intersection of the lines…

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Q: L₁ |x|dx

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Q: 3. 2y"" − 3y" – 3y² + 2y = (e*+ex)²

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Q: Which of the following is NOT a method for finding volume of solids of revolution? A) washer method…

A: Conic method

Q: -x/3 Jx/4 cscxcotxdx

A: topic- definite integral

Q: |x-4|dx

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