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A: We have to evaluate the indefinite integral
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A: Here, the solution to the DE is: y=C1e-2x+C2cos 2x+C3sin 2x...(1)
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A: Given query is to find the derivative of the expression.
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Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis
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A: greens theorem
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A: This question is related to definite integration, we will solve it using given information.
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A: Integral
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A: We can solve this as follows:
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Q: Find V · (V × F) if F(x, y, z) = 9 sin xi + cos(6x – 7y)j+ 4zk. - V · (V × F) =
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Q: 10 X=-3
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A: A detailed solution is given below.
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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||³ r(t) = 3 cos(2t)i+ 3 sin(2t)j + tk…
A: The given formula is: κt=r't×r''tr't3 And rt=3cos2ti+3sin2tj+tk As we know that; The Chain rule;…
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A: A detailed solution is given below.
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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy
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A: "Since you have asked multiple question, we will solve the first question for you. If you want any…
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Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…
A: we want to find the integral ∫03( 3x-6 -1 ) dx
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A: A detailed solution is given below.
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A: This is a problem related to dot and cross product of vector. Based on the general formula and…
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A: use derivative for finding the exact length.
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Q: INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) lim = lim Еquation…
A: This question is based on L hospitals rule.
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Q: 2. dy dx
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Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).
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Q: Find V × (V × F) if F(x, Y, z) 9xyj+ 5xyz k. ▼ × (V × F)
A: The detailed solution is given below Thank you
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A: Given; y^2+x^2=siny+4
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A: differential equation
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A: A detailed solution is given below.
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A: Differentiation
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A: We need to find value of derivative.
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.limit as x approaches 0 of x^6*cos(4/x)
- Evaluate in terms of Gamma function: y^5√(b^2 – y^2) dy LIMIT: 0 to ba) is f(x) = x3sin(1/x) uniformly continuous at (0,2] b) is g(x) = ln(x2+2) uniformly continuous at (-infinity, infinity) c) Decide if f(x) = x4sin(1/x3) is uniformly continuous at f : (0, infinity) --> RIf I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?
- Show that f(x,y) limit exists at (0,0) using epsilon-delta.Suppose ƒ is differentiable on (- ∞, ∞), ƒ(1) = 2, and ƒ'(1) = 3.Find the linear approximation to ƒ at x = 1 and use it to approximate ƒ(1.1).Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be the boundary of the region in the xy-plane that is bounded below by the x-axis, above by the graph of ƒ, and on the sides by the lines x = a and x = b. Show that ∫ƒ(x) dx = - ∮C y dx.
- a) f(a) exists b) f(x) is defined for 0<x<a c) f isn't continuous at x=a d)lim x-->a f(x) exists e)lim x-->a f(x)=f(a) which ones are true? could be up to four choices. explain.Prove: the limit as x approaches 0 1-cos(x)/x=0Use the definition to calculate the derivative of the criterion of the function f(x) = e14x. In addition, to calculate the respective limit, use the L'Hopital rule.