Find the linearization at x = a. f(x) = 9x', a = 1 (Use symbolic notation and fractions where needed.) L(x) =

Q: Find the point at which the line (-2, 2, 1) + t(5, –4, 3) intersects the plane -4x – 4y + z = -5.

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Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (If both values are the sa...

A: let the two numbers be x and y so  x×y=36sum=x+y since         xy=36⇒y=36x Substitute y value in sum...

Q: Consider the function (1 ifz1 Evaluate the definite integral. f(z) dz

A: we have to integrate fx 

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Q: Prove and derive how this hyperbolic function is formulated.

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Q: • Why do we need the Chain Rule in implicit differentiation? Show with an example and describe how t...

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Q: sechudu - 2tan".c -tan (sinhu) - C

A: Use the exponential form of sechu and easily prove the integral.I have used many inverse trigonometr...

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the ...

A: Given that: Distance from the bottom of the wall, x=8 ftLength of ladder, L=10 ftSliding speed of wa...

Q: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data...

A: Given query is to find the the linear function and time taken to completel full the balloon.

Q: Jsechudu = 2tan" +C = tan (sinhu) +C

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Q: lim(4x – 3) = 5 x→2

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Q: Consider the exponential function f(x) = 58(0.36)x. What is the 1-unit percent change for f

A: We can find the 1-unit percent change for f as below.

Q: Evaluate the integral 7sin^2(x)cos^2(x)dx, from 0 to pi/2

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Q: I. If z = In(xyz) implicitly defines a function, then ∂z/∂y = z / (z−y) II. Any function of the for...

A: This is a problem of partial derivative of the function. Based on the general formula used for PDE w...

Q: 10 and 11 triangle  Round your answers

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Q: Find the general solution to the differential equation. x' = t   4 + t x =

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Q: Evaluate: -3 3 dx x2 +x-2 -5

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Q: Find the parametric equations for the path of a particle that travels three quarters of the way arou...

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Q: Find the slope of the line tangent to the graph of y= sin3x at x=pie/6

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Q: (х+1)dy %3D (2xе* - ху - 2у)dx

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Q: Evaluate the limit. lim

A: We have to find limit of the given function.

Q: 4. The graph of y = (x² – 1)*(x² + 1)5 is shown below. Find the coordinates of the local max & min. ...

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Q: 19. What are all values of x for which [ P dt is equal to 0 ? (A) -2 only (B) 0 only (C) 2 only (D) ...

A: We have to find the value of x. 

Q: Iff (0) = g(0) = 0 and f" and g" are continuous, show that f(x)g"(x) dx = f(a)g'(a) – f'(a)g(a) + | ...

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Q: Use the Quotient Rule to find the derivative of the function. f(x) = f'(x) =

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Q: An object moves along a line so that its position at any time t is given by the function s ft), wher...

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Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos'x- 1) dx = 0

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Q: Write the following in terms of sine, using the cofunction relationship. cos(5π/9)

A: We have to write in sin form.

Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit. 7i im. Σ i = 1...

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Q: neat and orderly manner. linear equations:

A: Find the general solution  (D4 -2D3+D2)y= 0      

Q: 30 25 (11,20) 20 15 10 -5 -10 -15 -20 (19, -15) -25 -30 20 -15 -10 -5 5 10 15 20

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Evaluate the limit. V x2 + 3 lim 3x² + 1 x- 00

A: Given: - The equation is, limx→∞x2+33x2+1 To Evaluate: - The limit of the given equation,

Q: The graph of a feasible region is shown above. If the objective function is C = 3x + 4y, Ca) its max...

A: This is a problem related to maximum and minimum value of the graph function. Based on the coordinat...

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5 p...

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Q: 15? - 17 What is the exact value of sin (cos-le) where e = Provide your answer below:

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Q: The table shows the position of a cyclist. t (seconds) 0|123 4 |5 s (meters) 0|15 10 17 25 (a) Find ...

A: Given query is to find the average velocity using the table.

Q: Evaluate using trigonometric substitution ∫x^2/(16-4x^2)^3/2 dx

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Q: EXERCISE 2.3.6 Let f(x) = x and g(x) = 11r. Find Dlf(x) +g(x)]. %3D EXERCISE 2.3.7 Find D (x6-7x5 + ...

A: Given that:                                  6. f(x)=x-4 and g(x)=11x37. Dx(x6-7x5+13)8. f(x)=-9x2  ...

Q: Find dy for y = (4x +2)2. dy = (Simplify your answer.)

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Q: LY 5- -4 2- -5 -4 -3 -2 -14 -2+ -3

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Q: dx x² Vx² +9

A: Given that a integration of 1/(x2√x2+9). We know that Integration power rule is given  as - integrat...

Q: If f(x) = cos(x) Osxs 31/4 evaluate the Riemann sum with n = 6, taking the sample points to be left ...

A: Given:- f(x) = cos(x)  , 0≤ x≤ 3π/4  To find:- Evaluate the Riemann sum with n = 6 taking the sample...

Q: хр x?V25 - x

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Q: use implicit differentiation to find

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Q: Consider the cone z = √(x2 + y2). (a) Show that the tangent plane to this surface at any point (x0, ...

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Q: Sx (x +1) /3 dx

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Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in cm/...

A: Topic:- application of derivatives

Q: 10) Determine whether the series converges or diverges 2" n! n"

A: The given series,  ∑n=1∞2nn!nn

Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(B + H) + K. where t...

A: This question is related to function .solve in step 2.