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Q: HON 3 tan(e-*) dx Given: ex Find: du O e-*dx O -e-Xdx exdx O - e*dx

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Q: Find the solution of the following initial value problem: An 14a,-1- 49an- 2; ao = 0, a1 = 6 %3D an ...

A: Let us take an=rn. So, the characteristics equation will be       r2-14r+49=0⇒r=7, 7 Further, we hav...

Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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Q: dx x² Vx²-1 -2.

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Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x) ...

A: Here ,               We have given a function now we have to solve it by using definition of limit f...

Q: 4x 1.2) lim X4 yx-2

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Q: c. What is the height of the object at the highest point? d. When does the object strike the ground?...

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Q: Evaluate the integral of the improper fraction using partial fraction method - 2x + 6 + 1 d. 2x-8

A: We have to find given indefinite Integration.

Q: Prove that lim X-2 2x2-3x-2 = 5. x-2

A: Topic = Limits

Q: Solve the differential equation with appropriate method. Finalize answer free of logarithm and fract...

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Q: dx 3. The integral +1 reduces to where u = f(x) and for some constant k. Compute f(1). (a) (b) e +1 ...

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Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)...

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if f'x=06x1+2x2-4x3x21+2x22=06x1+...

Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: 1. The graph of a function f is shown. Verify that f satisfies the hypotheses of Rolle's Theorem on ...

A: Rolle's Theorem Let f(x) be a function that is continuous on [a, b]  and differentiable on (a, b). I...

Q: ax Evaluate • (1– 2x)² 1 2 2 O 1 O-1

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Q: Given: (2x3 (3- 5x4)’dx Find: Formula Ju'du 1 Ju'du 10 -2 |u'du 02 fư'au 2Ju’du

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Q: f(x) = { * ах 2 + ах —4, х> 2

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Q: dx Given: 2x- 3xlnx Find: du dx dx 3 X

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Q: Some scientists believe that the average temperature of the world has been rising steadily. The aver...

A: We have to find slope and T - imtercept And T (surface temperature in 2050) 

Q: Calculate the iterated integral. 36(u – v)³ du dv

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Q: Evaluate the integral V5+ 12x? - 4x xdx O 1 (2x2 – 3)/5+12x² – 4x4 + 14Arcsin V14(2x² – 3) +C 14 -3)...

A: Using integration of square root of a2 - x2

Q: 4 tanz dr 2. The value of the definite integral (b) (e) 1- (d) 0 (a) 1

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Q: (2.13) Compute Lp(t), where P is the regular tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1), (0...

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Q: A certain index I is a measure of soil moisture. An article described the rate of change of I with r...

A: dIdW=0.0634.6-I  

Q: Evaluate csc?x cot(cot x) dx. O- csc?(cot x) + C O cot(csc? x) + c O -In |sin(cot x)| +c O In sin(co...

A: Given query is to find indicated integral.

Q: Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure b...

A: Question : Graph the function, not by plotting points, but by starting from the graph of y = ex in t...

Q: 1. A strictly monotonic function is defined as a function that either always increases or always dec...

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Q: V sec3(In x) + sec2(In x) tan(In x) dx Given: 2x Find: du O tan(in x) dx X O tan(In x) dx 2x sec (In...

A: Given:     To determine: expression for du

Q: The growth in the number (in millions) of Internet users in a certain country between 1990 and 2019 ...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about * = x0 and then find the nth Taylor...

A: Let's find. 

Q: car rental agency rents 220 cars per day at a rate of ​$20 per day. For each ​$1 increase in​ rate, ...

A: Given query is to find the point where incom will be maximum.

Q: Evaluate csc?x cot(cot x) dx. O -In |sin(cot x)| +C O cot(csc?x) + C O - csc?(cot x) + C O In |sin(c...

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Q: 4. If u = f(x), then k +C for some constant k. dx = x* + 2x2 + 1 x² + 1 Compute kf (1). (a) 4 (b) – ...

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Q: y 4 A y = 4* 3 2 y = 2* 0.5 1

A: Given query is to find the area of shaded region.

Q: dP Recall that in a class this week, we discussed a problem where we are given = rP. K К -Р where r ...

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Q: ху — 1 dx x²y 1 xy2 dy = 0

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Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

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Q: Use sigma notation to write the Maclaurin series for the function. 7sin zx 7(– 1)*,2* (2k)! (2k + 1)...

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Q: An object is dropped from a tower, 576 ft above the ground. The object's height above ground t secon...

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Q: 45-48. Average values Find the following average values 45. The average distance between points of t...

A: Here, the given disk is: R:{(r,θ):0≤r≤a} which is a circle x2+y2=a2 Therefore, the average distance ...

Q: |d?y |dx2 K($) = Cos3 %3D

A: Given curve y=f(x)

Q: dw 3. (w² +4)Z

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Q: Calculate the respective marginal functions for the following total cost/revenue functions. you stat...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: 11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given inter...

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Q: 3. The area of the region under the curve y = 6z bounded by the lines z = 3 and z = 5 above the I-ax...

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Q: 1 x + 3

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Q: estimates used by climbers? Higher altitudes can present challenges to mountain climbers and hikers....

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Q: 1 dx ((x+1)²–1) 2

A:     ∫1x+12-12dx=∫ -14x+14x2+14x+2+14x+22dx=-∫14xdx+∫14x2dx+∫14x+2dx+∫14x+22dx=-14lnx-14x+14lnx+2-14x...

Q: A paint store sells 270 pails of paint per month at a price of $32 each. A customer survey indicates...

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