f(x) = 4e−2xsin(x2) 1. What is the first derivative of the equation? 2. Find f′(−1) manually.

Q: Calculate the vector line integral F. dr. where Fis the vector field (z+ Sy, 2z - y) and Cis the…

A: To find the value of the given line integral.

Q: x? V1-x2 dx Use trigonometric substitution

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Q: 2. - XGtx)

A: Explanation of the answer is as follows

Q: If the graph of y= ax+9 has a x-intercept at x= 3 and a vertical asymptote x =-3, the x+c a+c=

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Q: Use quadratic formula to find all the real zeroes of the 2nd degree polynomials 6x²-x-1

A: The given polynomial,      6x2-x-1

Q: A wooden rectangular box is to be made of lumber that is 2/3 in. thick. The inside length is to be 6…

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Q: Consider / sin'x cos?x dx. If we let u=cos x , the integrand can be transformed to A (u²+ 2u* +u6)…

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Q: 1-x² dx

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Q: Find the standard form of the equation of the hyperbola with •center at C(−2, 1), •a vertex at V(−2,…

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Q: Let f(x, y) = (x – 6)? Graph the boundary of the domain of f below. 7+ 5- 4 3 -7 -6 -5 -4 -3 -2 -1…

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Q: Find the indefinite integral. sinh(6 – 7x) dx

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Q: х-5 Determine the equations of any horizontal and vertical asymptotes of f(x)= x²- 25 horizontal: y…

A: To determine the equations of any horizontal and vertical asymptotes of fx=x-5x2-25.

Q: Solve the differential equation y tana+y = 3 sin r. %3D sin I A sin a B sin r + C Cos a c - sin I +…

A: We have to solve the differential equation: y'tanx+y=3sinx

Q: x³ sin (x²) dx is evaluated using IBP, the value of v du When A 2 sin (x2) -2 sin (x2) none of the…

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Q: Find the limit. lim tanh(x)

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Q: Find the limit. Use a graphing utility to verify your result. (Hint: Treat the expression as a…

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Q: Find or evaluate the integral by completing the square. (Round your answer to three decimal places.)…

A: Given problem:-

Q: A wooden rectangular box is to be made of lumber that is 2/3 in. thick. The inside length is to be 6…

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Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: The function f has the property that f(3)=2andf (3) = 4. Using a linear approximation to ff near x=3…

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Q: f(x) Let lim = 2. Find limits below. f(x) + 6x (a) lim 2.x f(3x) (b) lim I+0 5x

A: Use the limit given above and simplify limit for a and b .

Q: Question For the equation given below, one could use Newton's method as a way to approximate the…

A: We have to find the value of xn+1.

Q: QUESTION 1 At a price of $700 a supplier will supply 170 items. If the price decreases by $100, then…

A: Given query is to find linear function of supply.

Q: Find the absolute maximum and absolute minimum values of the function f(2) = a° – 6z² – 6 - 63z +4…

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Q: The​ half-life of a certain tranquilizer in the bloodstream is 45 hours. How long will it take for…

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Q: 4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1,…

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Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: 3. A boat sets sail moving at 65 mph due South. The ocean's current is flowing 15 mph due West. The…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 1 dx 4x2 – 1 XV

A: We have to determine integral

Q: Write the complex number in standard form. (2-J-15)* O -11+ /15i O 4- 15/5i O-11-4/15i O -11+4/15i…

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Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: 1 1. X CasCx y) dxdy. 0.

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Q: X is partly constant and varies as y when y= 3,x=7 And y=6,x=9 A. find the relationship between X…

A: We write x=ky+c when x is partly constant and varies as y Where x,y are variables and k,c are…

Q: 100e0.05z thousands of Over the next 5 years, a company projects its continuous flow of revenue to…

A: profit = revenue - cost here  revenue for next 5 year R(x) = 100e0.05x R(5) = 100e0.05(5) R(5) =…

Q: The absolute max occurs att The absolute min occurs at t

A: Follow the procedure given below.

Q: Given f''(x) 25 sin(5x) and f'(0) = - 1 and f(0) = 2. | Find f() 6.

A: Given query is to solve the differential equation and find the valu of indicated function.

Q: Find the quadratic function y=ax2+bx+c whose graph passes through the given points.   ​(1​,−1​),…

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Q: Determine the series' radius of convergence and interval of convergence: 1/2 (n)? (x+6)" 8" n=1

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Q: x² V1-x2 dx Use trigonometric substitution 2.

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Q: Solve the following ODE y' + tan(2 - x)y = 0 with initial condition y(0) = 3

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Q: a. Graph the function f(0) = 6 sin(0). 6- 4 -/2 3/2 -2 -4 -6 -8+ Clear All Draw: W b. Graph the…

A: We want to plot the graph.

Q: Convert the polar coordinates (3, 2) to Cartesian coordinates. (3, 0) (0, 3)

A: Given: (3,2)

Q: Convert the polar equation r² = 2tan 0 to a Cartesian equation. %3D Ox3 + y3 = 2 y x3 + xy² = 2 y…

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Q: 25 Simplify sec(arcsec 1/2 ). no solution -1/2 1/2

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Q: Convert the polar coordinates (1, 90 ) to Cartesian coordinates. (0, 1) (0, -1) (1, 0)

A: r= 1 and theeta= 90°

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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

Q: Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.)  lim x→∞ 2x tan(1/x)

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Q: x+x+1 Use partial fractions. 2x2+2+x3+x

A: The given integral is;  (x2+x+1)/(2x2+2+x3+x).

Q: Convert the polar coordinates (6, -T) to Cartesian coordinates. Leave answers in fractional form.…

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Q: g(b) Use the Substitution Formula, f(g(x)) g'(x) dx = f(u) du where g(x) = u, to evaluate the…

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