f(x) is shown in black (the thicker line), g(x) is shown in red (the thinner line). 6+ 5 3 N A + 5 6

Q: Condense the expression to the logarithmic of a single quantity 1/4{log7t + 3 log7(1-t)} - log7 (7

A: We have to find out

Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

A:

Q: f(x)=x√√x² +9 defined on the interval -5 ≤ x ≤ 6. f(x) is concave down on the interval x = f(x) is…

A: To find the extrema

Q: The plane y + z = 2 intersects the cylinder x2 + y2 = 5 in an ellipse. Find parametric equations for…

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Q: Evaluate the following integral. 4 √2 S 0 dx 16-x²

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Q: (x² + y² + x) dx + xycy = ax 0

A: The Solution is given below

Q: Find an equation of a plane through the point C-5, 4₁-32 Which is or thogonal to the line X= 5+-1₁…

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Q: What point on the parabola y = 4 - x² is closest to the point (4,4)? The point on the parabola y = 4…

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Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 12) ² €-8

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Q: 4. Find all local maximums and local minimums for f(x) = x³ - 2x² + x - 1.

A: We have given function fx=x3-2x2+x-1 Derivative of the function is given as f'x=ddxfx…

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

A:

Q: 4. If y = tan-¹(cos x), then dy = dx

A: As we know the Chain rule: fgx'=f'gx·g'x And Use the common derivatives.…

Q: Consider the function h(x) = f(x² - 1). Give the formula for the derivative h'(x).

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Q: A particle moves along the x-axis so that at time t≥ 0 its velocity is given by v(t) = 3t² − 48t +…

A:

Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

A: The velocity of the graph is increasing when the graph goes upwards.

Q: 118 SATU 101 X. A. f(x) = 3x^3+12x^2+5x+7 B. f(x) = 2x^2+5x+7 [hint: this function will always be…

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Q: Find a function whose graph is a parabola with vertex (4, -5) and that passes through the point…

A:

Q: 1. Find the second derivative of f(x), then find the x-values at which f(x) is concave up and the…

A: concavity of the fx=3x3+12x2+5x+7

Q: Find the indefinite integral. (Use C for the constant of integration.) sin³ 50 √ cos 50 dº X

A:

Q: 2. Solve the following integral (secx - tan x) secx dx O a. tanx + secx + C O b. secx - tanx + C O…

A: Solve the intregal

Q: 63. Between 0°C and 30°C, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is…

A:

Q: Part III. Find the 53rd derivative of sin x. Show your solution. I

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Q: m: b: (______) TAKE A TOUR y =____X +.

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Q: Find the equations of the lines tangent to the curve: 2e^x = y^2 − x, at x = 0.

A:

Q: Consider the following. f(x, y, z) = x²yz - xyz5, P(3, -1, 1), (a) Find the gradient of f. Vf(x, y,…

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Q: Consider the function f(x) For each prompt below, if no solution exists - enter "DNE". If there is…

A:

Q: Determine the behavior of the functions defined below. Note that it is common to write "g(x)→∞" to…

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Q: 7 The velocity of a moving vehicle is given by the equation v=(2t+3¹ The task is to: a) Use the…

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Q: Evaluate the following integral. * 1 π/4 SSS sin sin ™X sin 2y sin z dy dx dz 0 0 0 X 1元/4 SSS sin…

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Q: k=0 12( - 0.5) is an alternating geometric series, which converges diverges. Σ12(-0.5) - = k=0 Enter…

A:

Q: Find the derivative of the function g(x)=(x^2+4x+5)e^x g'(x)= Please answer ASAP and write neatly…

A: To find the derivative.

Q: The function f(x) has a continuous second derivative, and it satisfies f(-9) = -1, f'(-9) = 0 and…

A: Given, The function f(x) has a continuous second derivative, and it satisfies f(-9) = -1, f'(-9) =…

Q: In cylindrical coordinates, find the volume of the solid S enclosed by the cone and the sphere as…

A: Given : the cone z=r and the upper hemisphere z=2-r2.

Q: f(x)=x-x+2x-4

A:

Q: 3-8 Test the series for convergence or divergence. dhe tadt Hour 3.- + - + 1

A: 3. The given series is 47-48+49-410+411-....... We have to find the series is convergence or…

Q: Evaluate √ √R 6xy5 dydx R where the region is bounded by the curves y = = x² 1 and y = 1-². Sketch…

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Q: Find the equation (in terms of xx) of the line through the points (-1,4) and (2,-5) answer is -3x+1

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Q: If lim f(x) exists and fis not continuous X + b at b, what does b equal? 0 2 3 -1 إذا كانت (lim f(x…

A: Given graph:-

Q: Q4 d. lim ²+5x+6 x²-4 x112 e. limx→∞ (1-x²)³+40x6+x 3x6 +3

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Q: Consider the following function. f(x) = 16-x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all…

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Q: Find the domain of function s(x) = √-8 + 10x - - - 3x². Write your answer using interval notation in…

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Q: Let f(x) e = e-7x² Find F"(x). f"(x) = Find the x-value(s) where f"(x) = 0. (Enter your answers as a…

A: Topic = Derivative

Q: The same capacitor circuit is now charged up to 12V and the instantaneous voltage is v=121-e -e²²).…

A:

Q: + y² + z²) at (1, 0, 1). valuate the gradient of f(x, y, z) = = log(x².

A: Given query is to find the gradient.

Q: Find a function that satisfies the given conditions and sketch its graph. lim f(x)=0, lim f(x) = ∞o,…

A:

Q: Use l'Hôpital's Rule to find the limit. lim X-0 2 8x² cos (x) - 1 8x² 2 Xcos (x)-1 (Type an exact…

A: Given query is to find the limit of the expression.

Q: lve the exponential equation by expressing each side as a power of the same base and then equating…

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

Q: dx √ ₁ (1-x²7/01/2 0

A:

Q: 9. Consider the following 2 x 2 matrix A and basis S of R²: = [] and 5 = {[¹²₂] [²³₂]} The matrix A…

A: Given linear operator A=2456     and  basis   S= 1-2  ,3-7

Q: Consider the function f(x) = 3x³ - 2x on the interval [ - 3,3]. Find the average or mean slope of…

A: