Section B Work out the questions carefully. Show your working in the space provided. 1 Find the area of the shaded triangle. 1 cm A SHOT ON REDMI 7 AI DUAL CAMERA 1 cm B

Q: 1. Find f(x) if f'(x)=12x¹+3√x+7-2e -4 and f(1) = 4

A: Given f'x=12x3+3x+7x-2ex-4  and f1=4 To find f(x):

Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co C₁= C2= C3=…

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Q: Find the area of the region between the curves y = x and y = √x. Area between curves =

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Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

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Q: Describe the graph of the equation. r = − 12 i + (1 − t²)j + t k It is a parabola in the plane z = O…

A: Description about graph is given.

Q: d. Write the equations for any vertical asymptotes. e. What is the value of f"(x) on the interval -3…

A: We need to fill in the blanks.

Q: Verify Green's Theorem by evaluating both integrals ƏN [< y² dx + x² dy = √₂₁ / (™N - 3W) CIA dA əx…

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Q: Suppose that the revenue in selling x tables is equal to 200x – 0.25x“ dollars, and the cost of…

A: Here is the solution:

Q: (D² − 3D + 2)y = 2e¯* +8

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Q: Given a sin 6t and y = cos 6t, find the following derivatives as functions of t. dy/da 1 d'y/dx² =

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Q: y" + 6y' +5y=10sin (2x)

A: First find AE(Auxiliary equation) and PI ( Particular integral)  then CS ( Complete Solution) is PI…

Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 2t2i - 2tj + 0 18k (a) r'(t) (b) r"(t)…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: 2 Find az/ax if the equation yz - Inz = x + y

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Q: Consider the following. 5 - 10 5 -10 Find an equation for the hyperbola. Find the foci and…

A: Let's find.

Q: Find the limit. lim 1→2(t i - 5 j + t² k)

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Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i + 7 sin(t)j; t = 3 T() = N() =

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Q: Find DO NOT SIMPLIFY YOUR ANSWERS. 1. log √2x² + y + 2x² + y) + tan(x™ — ñ³) = sin¯^¹²(x² − 1) + ½ /

A: To dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: Which of the following is the derivative of x³ + 4x + 1? x² + 4x 3x² + 4 x²+4 3x²+4+1 3x² O

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Q: (a) Find the acceleration of the body each time the velocity is zero. Enter your answer as a list if…

A: Follow the procedure given below.

Q: [√x (x - 5)dx

A: ∫xx-5dx∫xx-5x dx∫x32-5x dx

Q: = The Taylor series for f(x) = √2x − x² at a : 1 is Σ Cn (x - 1)”. n=0 Find the first few…

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: 3. Evaluate the line integral Sc F. dr where F(x, y, z) = (e², xz, (x + y)) over the curve r(t) = t²…

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Q: Find the limit of the trigonometric function. lim 9 sin(x)

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Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

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Q: Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a…

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

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Q: 14. 2x²y-x³y' = y³

A: 2x2y-x3y' =y3

Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: Change the polar equation 2r = 2 + cos 0.(2r - 1) to Cartesian equation

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Q: [₁ [6x² arcsin(x)]dx

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Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 3 cost-2 sint,…

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: e3x-6-2, [2x - 5], √x²-9, if x ≤ 2 if 2 3

A: answer is in next step

Q: Convert the rectangular equation to polar form. xy=14

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Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Value of x for which series is convergent is given.

Q: Determine the sum of the following series. 31 10 Σ(1)

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Q: Determine whether F(x, y) = 4x²y i+ 9xy²j is a conservative vector field. If so, find a potential…

A: Determine whether F(x,y) is a conservative vector??

Q: (-3,0) y = h'(x) (0, -1) (-1,-2) (0, -2) (3,0)

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0, 3)…

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Q: y" + 6y' + 5y = 10sin (2x) A..! Inne(7)

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Q: Activity 2.2 For the given function sketch the graph; determine if f is continuous at xo and…

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Q: Find the derivative of the function. f(t) = (9t+ 9)2/3 f"(t): =

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Q: Consider the series (4x)n n n=1 Find the interval of convergence of this power series by first using…

A: Given problem:-