sin x lim x-0 X (Ans. 1)

Q: 12, y = xsin ²x (Ans. sin² x + x sin 2x)

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Q: Find the derivative of the function. a. y = ln(x² + 3x) b. Use the Product Rule to Find the…

A: Product rule :   =

Q: Find f if f'(x) Answer: f(x) = 16x³ + 16x + 6 and f(1)

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Q: Approximate the mass of the homogeneous lamina that has the shape of given surface S and density…

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Q: Use the Method of Coefficient to the general to the following non-homogeneous differential equation.…

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Q: What is the value of lim h→0 (1+h)6−1 ? h

A: Let,  This is  indeterminate form.

Q: If $800 is deposited into an account that pays 6%/a (per year) compounded monthly, how many months…

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Q: f(x) = Find the function f(x) described by the given initial value problem. f"(x)=0, f'(-2) = 4,…

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Q: The equation 4y2 +12y-9x2-15x + 45 = 0 can be changed into a vertex equation by completing the…

A: 0

Q: Find div F and curl F if F(x, y, z) = 3y³z³i - 14x5z³j - 6xy¹k. div F= curl F:

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Q: Consider the following initial value problem z" +52=0, 2(0)-6, z'(0)-5. (a) Using X for the Laplace…

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Q: Evaluate the integral [(6te7¹²) + (6e¯6t) j+ (7) k]dt. 0 ... [[(00²²³) + (60°) + (7) ►]α = 0+0¹0*…

A: We have definite integralWe have to evaluate it

Q: 10 cm 0⁰ 12 cm Figure 1 NOT TO SCALE 11 cm i) Find cos giving your answer in the form ii) Show that…

A: Solution is given below in step 2.

Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

A: Given vertices of triangle

Q: (2) The velocity function, in feet per second, is given for a particle moving in a straight line.…

A: Graph :-

Q: A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid…

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Q: QUESTION 2 Evaluate the expression without a log, 128 7 128 14 2

A: let

Q: From the graph of f(x), determine the graph of f'(x). -6 i पं -3 -2 1 y 5 4 3 2 O -1 -2 -3 -4 -5 2 W…

A: We need to find graph of f'(x) from given graph of f(x).Concept -If f(x) is increasing then slope…

Q: For the infinite sum-12, which statement is true? Σ •n=1_n²+1 n It is divegent using the Geometric…

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Q: Given the equation y The period is: = The horizontal shift is: 5 tan(4x12) units to the

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Q: Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the…

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Q: 1-A 0 Solve the equation 1 2 2-A 20 2 3-A

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: The population of a city, in millions, since 1990 has grown at a rate of P'(t) = 0.14e0.019 million…

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Q: Using the graph of f(x), what is the limx→→2 f(x) ? -2 2 0 -2 0 2

A: Suppose is a function of real variable and  is a point in the domain of the function. If and both…

Q: Find the x— and y-coordinates of the inflection point of f(x). (x, y) ( On what interval(s) of x is…

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Q: The following hyperbola has a vertical transverse axis: (x+2)² (+7) _ =1. 17 16

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Q: Use cylindrical coordinates. Evaluate √x² + y² dv, where E is the region that lies inside the…

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Q: Find the exact value of y, or state that y is undefined. y = sin-¹ (4) -1 000 undefined 0 4 Л

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Q: Find a formula for Ry and compute the area under the graph of f(x) = 24x² - 4 over [2, 5] as a…

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Q: For the function given below, find a formula for the Riemann sum obtained by dividing the int curve…

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Q: Calculate the moment of inertia of the shaded area about the x-axis. 96 mm Answer: Ix = 96 mm 57 mm…

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Q: Find the volume of rotation for the region enclosed by the graphs of y = x³ + 7, y =9-x² and x = 3…

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Q: What are the foci of the following ellipse? 25x² - 50x+9y² - 90y=-25

A: 25x2−50x+9y2−90y=−25

Q: If limx→a f(x) = 3 and lim,→ g(x) = 2, then what is the value of lim (-3[ƒ(x)]²+49(x)) ? x→a -7 None…

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Q: Identify and express the function from the graph given either as a sine or cosine function. 2π -7514…

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Q: Find f if f" (t) = 2et + 3 sin(t), f(0) = -10, f(π) = = -5. (Notice that they did not give you any…

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Q: If [34, f(x) dx = 19, then compute the value of the following definite integral. 6 fºr f(5x + 4) dx

A: Using properties of definite integral, we can solve the question.According to our guidelines, we…

Q: QUESTION 19 Use an appropriate identity to find the exact value of the expression. COS Ela J2ܢ…

A: We have to find value of Cos(π/12)

Q: 10. Find the average value of f(x, y) = xy on the quarter circle x² + y² = 1 in the first quadrant

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Q: Identify and express the function from the graph given as a sine

A: We have to express the function as a sin function.

Q: A cylindrical drill with radius 2 is used to bore a hole through the center of a sphere of radius 4.…

A: Given that:

Q: A cylindrical drill with radius 2 is used to bore a hole through the center of a sphere of radius 4.…

A: Given that:

Q: Use the integration Factor Method to find the general solution of y +x у=4х2

A: Given

Q: π Compute uv if u and v are unit vectors and the angle between them is 4 u v= (Type an exact answer,…

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Q: Integrate G(x,y,z) = z over the parabolic cylinder y=z², 0≤x≤ 4, Oszs√2.

A: Integrate G(x,y,z)=zover the parabolic cylinder y=z2,0≤x≤4,0≤z≤2.

Q: Evaluate the integral by making an appropriate change of variables.     R5e4x + 4y dA,  where R is…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. x =…

A: Using iterated integral, we can find the required area.

Q: (11) Find the indefinite integral 2 (a)fese ² x di dt cot³ x

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Q: The curves r₁(t) = (3t, t¹, 2t³) and F₂(t) = (sin(–5t), sin(2t), t — π) intersect at the origin. ㅠ…

A: These derivatives represent tangent vector to the curves at the origin.

Q: Use the Trapezoidal Rule to approximate (2x² + 1) dx using n = 4. Round your answer to the nearest…

A: We can find the integral using trapezoidal rule and it's exact value and then compare them.